{"total":10,"items":[{"citing_arxiv_id":"2605.22728","ref_index":20,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"A $\\operatorname{prox}$-Based Semi-Smooth Newton Method for TV-Minimization","primary_cat":"math.NA","submitted_at":"2026-05-21T17:00:56+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"A prox-based semi-smooth Newton method for TV-minimization that is globally well-posed and locally superlinearly convergent under finite element discretization, extending to broader convex problems.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.16684","ref_index":144,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"GPU Performance of an Entropy-Stable Discontinuous Galerkin Euler Solver with Non-Conservative Terms","primary_cat":"math.NA","submitted_at":"2026-05-15T22:43:11+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"GPU port of entropy-stable DG Euler solver with non-conservative buoyancy terms reaches nearly 70% of 64-bit peak on A100 volume kernels, delivers 10x speedup and 13x better energy efficiency versus CPU, and preserves symmetry-based flux savings.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.12095","ref_index":9,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Leak localisation with a measure source convection-diffusion model","primary_cat":"math.AP","submitted_at":"2026-05-12T13:13:34+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"A convection-diffusion model with sparsity-regularized Radon measure source recovers point gas leak locations and intensities from concentration measurements while jointly estimating convection and diffusion parameters.","context_count":1,"top_context_role":"method","top_context_polarity":"use_method","context_text":"≤ ∥𝑘∥ 𝐿∞ (Ω𝑇 ) ∥∇ ˜𝑢∥ 𝐿𝑝 (Ω𝑇 ) ∥∇𝑣 Ω ∥𝐿𝑝′ (Ω𝑇 ), ∫ Ω𝑇 (𝑐· ∇ ˜𝑢)𝑣 Ω d𝜉d𝑡 ≤ ∥𝑐∥ 𝐿∞ (Ω𝑇 ;ℝ𝑑 ) ∥∇ ˜𝑢∥ 𝐿𝑝 (Ω𝑇 ) ∥𝑣 Ω ∥𝐿𝑝′ (Ω𝑇 ),and ∫ Σ1 ˜𝑢| Σ1𝑣 Γ1 d𝜎d𝑡 ≤ ∥ ˜𝑢| Σ1 ∥𝐿2 (Σ1 ) ∥𝑣 Γ1 ∥𝐿2 (Σ1 ) . By trace theorem and Poincaré inequality, ∥ ˜𝑢| Σ1 ∥𝐿2 (Σ1 ) + ∥𝑣 Ω ∥𝐿𝑝′ (Ω𝑇 ) ≤𝐶 𝑃 ∥ ˜𝑢∥ 𝑈 + ∥𝑣 Ω ∥𝑊 \u0001. Again, by the Poincaré inequality [9, Corollary 9.19] on𝑊 1,𝑝′ 0 (Ω) , we have ∥𝑣∥ 𝐿𝑝′ (Ω𝑇 ) ≤𝐶 𝑃 ∥∇𝑣∥ 𝐿𝑝′ (Ω𝑇 ), so all three terms are bounded by 𝐶∥𝜕𝑡 ˜𝑢∥ 𝐿2 (𝐼;𝑊 −1,𝑝′ (Ω) ) + (∥𝑘∥ 𝐿∞ (Ω𝑇 ) + ∥𝑐∥ 𝐿∞ (Ω𝑇 ;ℝ𝑑 ) ) ∥∇˜𝑢∥ 𝐿𝑝′ (Ω𝑇 ) \u0001 ∥𝑣∥ 𝑊 , for some𝐶>0depending only onΩ,Γ 2, 𝑝, 𝑇. Taking the supremum over∥𝑣∥ 𝑊 =1gives ∥𝑒 (𝑢) (𝑢, 𝜇, 𝑘, 𝑐) ˜𝑢∥ 𝑊 ∗ ≤𝐶 1+ ∥𝑘∥ 𝐿∞ (Ω𝑇 ) + ∥𝑐∥ 𝐿∞ (Ω𝑇 ;ℝ𝑑 ) \u0001 ∥ ˜𝑢∥ 𝑈 ,"},{"citing_arxiv_id":"2605.08714","ref_index":4,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Well-posedness and regularity for seminlinear time-dependent second and fourth order in space equations","primary_cat":"math.AP","submitted_at":"2026-05-09T05:53:35+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"Existence and uniqueness of weak solutions are proved for the semilinear time-dependent equation with second or fourth order diffusion and cubic nonlinearity, for both smooth and rough initial data via Faedo-Galerkin and compactness methods.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"33-76,url:https://doi.org/10.1016/0001- 8708(78)90130-5. [3] (1975), \"Nonlinear diffusion in population genetics, combustion, and nerve pulse propa- gation\",Partial differential equations and related topics (Program, Tulane Univ., New Orleans, La., 1974), vol. 446, Lecture Notes in Math. Springer, Berlin-New York, pp. 5-49,url:https: //doi.org/10.1007/BFb0070595. [4] H. Brezis (2011),Functional analysis, Sobolev spaces and partial differential equations, Uni- versitext, Springer, New York,url:https://doi.org/10.1007/978-0-387-70914-7. [5] C. Carstensen and N. Nataraj (2021), A priori and a posteriori error analysis of the Crouzeix- Raviart and Morley FEM with original and modified right-hand sides,Comput. Methods Appl."},{"citing_arxiv_id":"2605.06518","ref_index":134,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Absolute continuity of generalized Wasserstein barycenters of finitely many measures","primary_cat":"math.DG","submitted_at":"2026-05-07T16:26:17+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Generalized Wasserstein barycenters on Riemannian manifolds are absolutely continuous when all input measures are absolutely continuous, for strictly convex cost profiles h with singularity at zero, via a geometric approximation approach.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.25965","ref_index":2,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Adversarial Robustness of NTK Neural Networks","primary_cat":"stat.ML","submitted_at":"2026-04-28T04:49:31+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"NTK networks achieve minimax optimal adversarial regression rates in Sobolev spaces with early stopping, but minimum-norm interpolants are vulnerable.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.19521","ref_index":124,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Singularities in phase separation models: a spectral element approach for the nonlocal Cahn-Hilliard equation","primary_cat":"math.NA","submitted_at":"2026-04-21T14:43:47+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"A pseudospectral multishape method is developed to accurately approximate singular convolution operators in the nonlocal Cahn-Hilliard equation, enabling efficient high-resolution phase separation simulations.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.08904","ref_index":15,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Existence and uniqueness of nonlocal nonlinear conservation laws via fixed-point methods","primary_cat":"math.AP","submitted_at":"2026-04-10T03:12:19+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Existence and uniqueness of weak entropy solutions for nonlocal nonlinear scalar conservation laws is proven on short time horizons via fixed-point methods, extending to any finite horizon under additional assumptions.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"≤δ∥∂ 3 ˜Φ∥L1(ΩT ;L∞( ˜U)) + ZZZ (−δ,δ)n+2 \u0010Z T 0 Z Rn ˜Φ(t−s,x−y,·)− ˜Φ(t,x,·) L∞(U) dxdt \u0011 Θδ(s,y, v) dsdydv ≤δ∥∂ 3Φ∥L1(ΩT ;L∞( ˜U)) + sup y∈[−δ,δ]n, s∈(−δ,δ) ∥ ˜Φ(· −s,∗ −y, ⋆)− ˜Φ(·,∗, ⋆)∥ L1(ΩT ;L∞(U)) . The first term vanishes asδ→0, since∥∂3Φ∥L1(ΩT ;L∞( ˜U)) is finite by Theorem 4.1. The second term vanishes by theL 1-continuity of translations; see [15, Lemma 4.3]. We now turn to Eq. (23). The same argument as above, now applied toDivΦinstead ofΦ, yields DivΦ δ −DivΦ L1(ΩT ;L∞(U)) = Z T 0 Z Rn ess-sup u∈U |DivΦ δ(t,x, u)−DivΦ(t,x, u)|dxdt.(25) SinceΦis regular enough for the divergence to commute with the convolution, we may writeDivΦ δ = DiveΦ∗Θ δ and use R Θδ = 1to obtain (25)= Z T 0 Z Rn"},{"citing_arxiv_id":"2603.07218","ref_index":20,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"An Investigation of Stabilization Scaling in Finite-Strain Virtual Element Methods for Hyperelasticity","primary_cat":"math.NA","submitted_at":"2026-03-07T13:57:53+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"A decoupled kernel-only stabilization for finite-strain VEM hyperelasticity is introduced that scales deviatoric terms by shear modulus with geometry weights and volumetric terms independently by bulk modulus, with uniform stability proven under polygon regularity.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2602.21414","ref_index":8,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"The Influence of Exclusion Zones on the Coexistence of Predator and Prey with an Allee Effect","primary_cat":"math.AP","submitted_at":"2026-02-24T22:39:21+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A predator-prey reaction-diffusion model with Allee effect and exclusion zones admits positive coexistence equilibria when the predator-free area is sufficiently large, proven globally via topological degree theory, with non-vanishing predator populations as the predation area shrinks.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}