Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time | Paper Citation Record

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This paper cites Data assimilation in 2D nonlinear advection diﬀusion equations, using an explicit 10 stabilized leapfrog scheme run backwrd in time.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Data assimilation in 2D nonlinear advection diﬀusion equations, using an explicit 10 stabilized leapfrog scheme run backwrd in time

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Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Opportunistic capacity and error exponent regions for compound channel with feedback

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Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Data assimilation in 2D incompressible Navi er-Stokes equations, using a stabilized explicit O(∆ t)2 leapfrog ﬁnite diﬀerence scheme run backward in time

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This paper cites Diﬀerence Methods for Initial V alue Problems.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Diﬀerence Methods for Initial V alue Problems

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This paper cites M´ ethode de Quasi-R´ eversibilit´ e et Applications [The Method of Quasi- Reversibility and Applications].

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time M´ ethode de Quasi-R´ eversibilit´ e et Applications [The Method of Quasi- Reversibility and Applications]

Reference 6

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Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Sur l’approximation de la solution d’´ equatio ns d’´ evolution coupl´ ees

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This paper cites Coupled sound and heat ﬂow and the method of le ast squares.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Coupled sound and heat ﬂow and the method of le ast squares

Reference 8

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This paper cites Tracking the model: data assimilation by artiﬁ- cial neural network.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Tracking the model: data assimilation by artiﬁ- cial neural network

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This paper cites A machine learning a ugmented data assimilation method for high resolution observations.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time A machine learning a ugmented data assimilation method for high resolution observations

Reference 10

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This paper cites Data Assimilation for Ge ophysical Fluids.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Data Assimilation for Ge ophysical Fluids

Reference 11

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This paper cites Physics-i nformed neural networks for mul- tiphysics data assimilation with application to subsurfac e transport.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Physics-i nformed neural networks for mul- tiphysics data assimilation with application to subsurfac e transport

Reference 12

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This paper cites Deep data assimilation: int egrating deep learning with data assimilation.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Deep data assimilation: int egrating deep learning with data assimilation

Reference 13

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This paper cites Data Assimilation with Deep Neural Nets Informed by Nudging.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Data Assimilation with Deep Neural Nets Informed by Nudging

Reference 14

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This paper cites A novel neural network traini ng framework with data assimi- lation.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time A novel neural network traini ng framework with data assimi- lation

Reference 15

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Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Iterative methods f or data assimilation for Burgers’ equa- tion

Reference 16

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This paper cites A nudging-based data assimilation met hod for oceanographuc problems: the back and forth nudging (BFN) algorithm.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time A nudging-based data assimilation met hod for oceanographuc problems: the back and forth nudging (BFN) algorithm

Reference 17

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This paper cites Unsteady adjoint method for the optimal control of advection and Burg- ers’ equation using high order spectral diﬀerence method.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Unsteady adjoint method for the optimal control of advection and Burg- ers’ equation using high order spectral diﬀerence method

Reference 18

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This paper cites The back and forth nudging algorithm f or data assimilation problems: theoretical results on transport equations.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time The back and forth nudging algorithm f or data assimilation problems: theoretical results on transport equations

Reference 19

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This paper cites An evolution of the back and f orth nudging for geophysical data assimilation: application to Burgers equation and compari son.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time An evolution of the back and f orth nudging for geophysical data assimilation: application to Burgers equation and compari son

Reference 20

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This paper cites Numerical aspects of lar ge-time optimal control of Burgers’ equation.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Numerical aspects of lar ge-time optimal control of Burgers’ equation

Reference 21

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This paper cites Filtered gradient algorithms for inv erse design problems of one-dimensional Burgers’ equation.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Filtered gradient algorithms for inv erse design problems of one-dimensional Burgers’ equation

Reference 22

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This paper cites Special issue o n inverse problems in geosciences.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Special issue o n inverse problems in geosciences

Reference 23

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This paper cites Contaminant source identiﬁc ation in acquifers: a critical view.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Contaminant source identiﬁc ation in acquifers: a critical view

Reference 24

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This paper cites Non-point cont aminant source identiﬁcation in an acquifer using the ensemble smoother with multiple data ass imilation.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Non-point cont aminant source identiﬁcation in an acquifer using the ensemble smoother with multiple data ass imilation

Reference 25

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This paper cites Properties of advecti on algorithms in the context of varia- tional data assimilation.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Properties of advecti on algorithms in the context of varia- tional data assimilation

Reference 26

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This paper cites Compensating operators and stable backwar d in time marching in nonlinear parabolic equations.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Compensating operators and stable backwar d in time marching in nonlinear parabolic equations

Reference 27

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This paper cites Stable explicit time-marching in well-pos ed or ill-posed nonlinear parabolic equa- 11 tions.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Stable explicit time-marching in well-pos ed or ill-posed nonlinear parabolic equa- 11 tions

Reference 28

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This paper cites Stable explicit marching scheme in ill-pos ed time-reversed viscous wave equations.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Stable explicit marching scheme in ill-pos ed time-reversed viscous wave equations

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:55:55.587949Z

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This paper cites Stabilized Richardson leapfrog scheme in e xplicit stepwise computation of forward or backward nonlinear parabolic equations.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Stabilized Richardson leapfrog scheme in e xplicit stepwise computation of forward or backward nonlinear parabolic equations

Reference 30

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Observation 57ad6808-7fe2-4dfd-81a3-ffa8ca2fd4d7 · outbound

This paper cites Stable explicit stepwise marching scheme i n ill- posed time-reversed 2D Burgers’ equation.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Stable explicit stepwise marching scheme i n ill- posed time-reversed 2D Burgers’ equation

Reference 32

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This paper cites Computing ill-posed time-reversed 2D Navi er-Stokes equations, using a stabilized explicit ﬁnite diﬀerence scheme marching backward in time.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Computing ill-posed time-reversed 2D Navi er-Stokes equations, using a stabilized explicit ﬁnite diﬀerence scheme marching backward in time

Reference 33

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This paper cites Stabilized leapfrog scheme run backward in time, and the explicit O(∆ t)2 stepwise computation of ill-posed time-reversed 2D Navier-Stokes e quations.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Stabilized leapfrog scheme run backward in time, and the explicit O(∆ t)2 stepwise computation of ill-posed time-reversed 2D Navier-Stokes e quations

Reference 34

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This paper cites Non-Standard and Improperly Pose d Problems.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Non-Standard and Improperly Pose d Problems

Reference 35

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This paper cites Some remarks on ill-posed problems for viscou s ﬂuids.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Some remarks on ill-posed problems for viscou s ﬂuids

Reference 36

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This paper cites Logarithmic convexity and other techniques a pplied to problems in continuum echan- ics.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Logarithmic convexity and other techniques a pplied to problems in continuum echan- ics

Reference 37

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Observation dd19b689-903f-4b56-84db-7fc412b705f2 · outbound

This paper cites On the stability of solutions of the N avier-Stokes equations backward in time.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time On the stability of solutions of the N avier-Stokes equations backward in time

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T14:55:55.509668Z

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This paper cites Uniqueness and continuous dependence criter ia for the Navier-Stokes equations.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Uniqueness and continuous dependence criter ia for the Navier-Stokes equations

Reference 39

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This paper cites Reconstructing the past from imprecise kno wledge of the present: Eﬀective non- uniqueness in solving parabolic equations backward in time.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Reconstructing the past from imprecise kno wledge of the present: Eﬀective non- uniqueness in solving parabolic equations backward in time

Reference 40

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Observation 0e60696a-a42f-4ee9-b7f5-be353903b802 · outbound

This paper cites Computing small solutions of Burgers’ equat ion backwards in time.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Computing small solutions of Burgers’ equat ion backwards in time

Reference 41

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Observation 09d1e1f8-01e9-437e-93ba-fb22a18e8dcb · outbound

This paper cites Stability estimates for B urgers-type equations backward in time.

Data assimilation in 2D nonlinear coupled sound and heat flow, using a stabilized explicit finite difference scheme marched backward in time Stability estimates for B urgers-type equations backward in time

Reference 42

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