Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T16:31:14.726867Z
Paper Citation Record · LEDGER
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background
As of 16 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 1 inbound Pith citation observation for arXiv:2509.04850.
A citation records a reference. It does not transfer a finding from one paper to another.
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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-04T22:16:40.198457Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-04T22:16:41.176177Z
Reference resolution
31 of 31 outbound references displayed
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External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 304b88d6-0f3a-4eeb-9fae-533af516e017 · outbound
This paper cites Local and global solvability of some parabolic systems modelling chemo- taxis.Advances in Mathematical Sciences and Applications, 8:715–743, 1998.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Local and global solvability of some parabolic systems modelling chemo- taxis.Advances in Mathematical Sciences and Applications, 8:715–743, 1998
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:15.225584Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 25ae3848-a688-45dd-8549-7733a81f4a36 · outbound
This paper cites Global solutions to some parabolic-elliptic systems of chemotaxis.Advances in Mathematical Sciences and Applications, 9:347–359, 1999.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Global solutions to some parabolic-elliptic systems of chemotaxis.Advances in Mathematical Sciences and Applications, 9:347–359, 1999
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:15.209931Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation cc33f373-ac15-4530-8a6c-eef514d9fdd8 · outbound
This paper cites Logarithmic stability in determining the time- dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to- Neumann map.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Logarithmic stability in determining the time- dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to- Neumann map
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:15.194000Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 92689dcd-84e8-4a65-9338-2cc15992a03e · outbound
This paper cites Inverse problems for coupled nonlocal nonlinear systems arising in mathematical biology.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Inverse problems for coupled nonlocal nonlinear systems arising in mathematical biology
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T16:31:14.602120Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fce37136-47f5-486e-9f9b-c162da5457e8 · outbound
This paper cites Global behaviour of a reaction-diffusion system modelling chemotaxis.Mathematische Nachrichten, 195(1):77–114, 1998.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Global behaviour of a reaction-diffusion system modelling chemotaxis.Mathematische Nachrichten, 195(1):77–114, 1998
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:15.178927Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3d565f34-b974-45be-a316-8bc78783c70d · outbound
This paper cites Singularity patterns in a chemotaxis model.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Singularity patterns in a chemotaxis model
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:15.164542Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation fc236643-5f2e-4b6a-a5dc-b638f26edc05 · outbound
This paper cites From 1970 until present: the Keller-Segel model in chemotaxis and its consequences.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background From 1970 until present: the Keller-Segel model in chemotaxis and its consequences
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T16:31:14.617110Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 174f8d4c-b6b6-4ead-829c-611217ef8eec · outbound
This paper cites On uniqueness in inverse problems for semilinear parabolic equations.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background On uniqueness in inverse problems for semilinear parabolic equations
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:15.138577Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4af928ca-ca68-4bb7-9dbc-ca044fb20dd1 · outbound
This paper cites Global existence in a fully parabolic attraction-repulsion chemotaxis system with singular sensitivities and proliferation.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Global existence in a fully parabolic attraction-repulsion chemotaxis system with singular sensitivities and proliferation
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:15.122138Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 658b69de-f130-4c8e-ae66-895a388046d7 · outbound
This paper cites Boundedness of the attraction–repulsion Keller–Segel system.Journal of Mathematical Analysis and Applications, 422(2):1463–1478, 2015.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Boundedness of the attraction–repulsion Keller–Segel system.Journal of Mathematical Analysis and Applications, 422(2):1463–1478, 2015
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:15.106545Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d1f325fc-8a42-4800-8a25-7d40649cc4c5 · outbound
This paper cites Initiation of slime mold aggregation viewed as an instability.Journal of theoretical biology, 26(3):399–415, 1970.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Initiation of slime mold aggregation viewed as an instability.Journal of theoretical biology, 26(3):399–415, 1970
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T16:31:14.633758Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4f7cce4c-4bd6-4d4b-8431-2fc488ea0b27 · outbound
This paper cites Model for chemotaxis.Journal of theoretical biology, 30(2):225–234, 1971.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Model for chemotaxis.Journal of theoretical biology, 30(2):225–234, 1971
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:15.079963Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e94257f2-8260-4264-8d86-2993cb8472b9 · outbound
This paper cites Traveling bands of chemotactic bacteria: a theoretical analysis.Journal of theoretical biology, 30(2):235–248, 1971.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Traveling bands of chemotactic bacteria: a theoretical analysis.Journal of theoretical biology, 30(2):235–248, 1971
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:15.062531Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2746ad6f-975c-4ada-8c23-97da89fab3bb · outbound
This paper cites Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations.Revista Matem´ atica Iberoamericana, 37(4):1553–1580, 2020.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations.Revista Matem´ atica Iberoamericana, 37(4):1553–1580, 2020
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:15.045756Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ac0ff6ab-2724-4306-b295-251d7f301ef6 · outbound
This paper cites Inverse problems for elliptic equations with power type nonlinearities.Journal de math´ ematiques pures et appliqu´ ees, 145:44–82, 2021.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Inverse problems for elliptic equations with power type nonlinearities.Journal de math´ ematiques pures et appliqu´ ees, 145:44–82, 2021
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:15.030639Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 96b7abdb-1de3-4604-af42-51427f5bf05b · outbound
This paper cites Roles of density-related diffusion and signal-dependent motilities in a chemotaxis–consumption system.Calculus of Variations and Partial Differential Equations, 63(8):195, 2024.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Roles of density-related diffusion and signal-dependent motilities in a chemotaxis–consumption system.Calculus of Variations and Partial Differential Equations, 63(8):195, 2024
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:15.016157Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 64f7b542-a12e-4578-8164-0a5a41977a29 · outbound
This paper cites On inverse problems in predator-prey models.Journal of Differential Equations, 397:349–376, 2024.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background On inverse problems in predator-prey models.Journal of Differential Equations, 397:349–376, 2024
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:14.999874Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ab41b872-8c1d-4d96-aefe-485468b85e68 · outbound
This paper cites On inverse problems in multi-population aggregation models.Journal of Differential Equations, 414:94–124, 2025.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background On inverse problems in multi-population aggregation models.Journal of Differential Equations, 414:94–124, 2025
Reference 18
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T16:31:14.665845Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 65039e3e-6919-4497-972a-dd7e272b75bb · outbound
This paper cites On the simultaneous recovery of environmental factors in the 3D chemotaxis-navier-stokes models.Communications on Analysis and Computation, 2(1):30–47, 2024.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background On the simultaneous recovery of environmental factors in the 3D chemotaxis-navier-stokes models.Communications on Analysis and Computation, 2(1):30–47, 2024
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:14.972797Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 69c22a83-3dfc-42db-b175-f51bd5828ecb · outbound
This paper cites Large-time behavior of an attraction– repulsion chemotaxis system.Journal of Mathematical Analysis and Applications, 426(1):105–124, 2015.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Large-time behavior of an attraction– repulsion chemotaxis system.Journal of Mathematical Analysis and Applications, 426(1):105–124, 2015
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:14.955466Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c80f09b8-244f-4581-98aa-7b022d3209e4 · outbound
This paper cites Global boundedness in a fully parabolic attraction– repulsion chemotaxis model.Mathematical Methods in the Applied Sciences, 38(12):2537–2546, 2015.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Global boundedness in a fully parabolic attraction– repulsion chemotaxis model.Mathematical Methods in the Applied Sciences, 38(12):2537–2546, 2015
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:14.939144Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4c8b9994-cf35-4847-b727-e226321ad0a8 · outbound
This paper cites Determining a parabolic system by boundary observation of its non-negative solutions with biological applications.Inverse Problems, 40(2):025009, 2024.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Determining a parabolic system by boundary observation of its non-negative solutions with biological applications.Inverse Problems, 40(2):025009, 2024
Reference 22
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T16:31:14.685894Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b0247f01-9066-4d79-8c75-a819660124a1 · outbound
This paper cites Determining both sound speed and internal source in thermo-and photo-acoustic tomography.Inverse Problems, 31(10):105005, 2015.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Determining both sound speed and internal source in thermo-and photo-acoustic tomography.Inverse Problems, 31(10):105005, 2015
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:14.912717Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 79e69c65-f283-4b52-86be-8dd05ac7eed3 · outbound
This paper cites Classical solutions and steady states of an attraction– repulsion chemotaxis in one dimension.Journal of biological dynamics, 6(sup1):31–41, 2012.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Classical solutions and steady states of an attraction– repulsion chemotaxis in one dimension.Journal of biological dynamics, 6(sup1):31–41, 2012
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:14.896738Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8085787e-f6f7-420b-85ad-70dd4eb5230d · outbound
This paper cites Mathematical analysis of the dynamics of some reaction-diffusion models for infectious diseases.Journal of Differential Equations, 370:424–469, 2023.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Mathematical analysis of the dynamics of some reaction-diffusion models for infectious diseases.Journal of Differential Equations, 370:424–469, 2023
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:14.881099Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2d66d99c-f898-4eb2-b9dc-ef6f32c22443 · outbound
This paper cites Chemotactic signaling, microglia, and Alzheimer’s disease senile plaques: Is there a connection?Bulletin of mathematical biology, 65(4):693–730, 2003.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Chemotactic signaling, microglia, and Alzheimer’s disease senile plaques: Is there a connection?Bulletin of mathematical biology, 65(4):693–730, 2003
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:14.864727Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 40d94c25-80f4-461d-81e2-c5a7925f7779 · outbound
This paper cites Global existence and blow-up of radial solutions to a parabolic-elliptic system of chemotaxis.Adv.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Global existence and blow-up of radial solutions to a parabolic-elliptic system of chemotaxis.Adv
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:14.847165Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation cca9f564-3f0a-4cfc-99fb-9d1eef0f5d3e · outbound
This paper cites Volume-filling and quorum-sensing in models for chemosensitive movement.Can.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Volume-filling and quorum-sensing in models for chemosensitive movement.Can
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:14.832368Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 27cb8b85-ecd4-41e4-b42f-290d8cbf95a3 · outbound
This paper cites Well-posedness for a model derived from an attraction– repulsion chemotaxis system.Journal of Mathematical Analysis and Applications, 423(1):497–520, 2015.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Well-posedness for a model derived from an attraction– repulsion chemotaxis system.Journal of Mathematical Analysis and Applications, 423(1):497–520, 2015
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:14.817963Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e16f59fc-2890-4d85-af9f-49e2c928dc00 · outbound
This paper cites Competing effects of attraction vs.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background Competing effects of attraction vs
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:14.802501Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0af60069-3b80-4bd2-8f08-c6f28763cdd0 · outbound
This paper cites A parabolic–elliptic–elliptic attraction– repulsion chemotaxis system with logistic source.Journal of Mathematical Analysis and Applications, 455(1):650–679, 2017.
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background A parabolic–elliptic–elliptic attraction– repulsion chemotaxis system with logistic source.Journal of Mathematical Analysis and Applications, 455(1):650–679, 2017
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:31:14.786960Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
Observation 4ee948d8-bc88-4c34-a7ec-ef1f5a86b8fe · inbound
Unveiling Biological Models Through Turing Patterns cites this paper.
Unveiling Biological Models Through Turing Patterns Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background
Reference 16
- Resolution
- verified exact
- local_arxiv, observed 2026-08-04T22:16:41.248081Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.