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Optimal Control of the Viscous Wave Equation via the Pontryagin Maximum Principle
Numerical Methods for Partial Differential Equations, Volume 42, Issue 3, May 2026.ABSTRACT A tracking‐type optimal control problem governed by the viscous wave equation with a distributed‐source control and L2$$ {L}^2 $$‐L1$$ {L}^1 $$ control costs is investigated. For this class of PDE‐constrained linear‐convex problems, a Pontryagin maximum principle (PMP) in the PDE setting is derived, and it is shown that the pointwise ...
A. Borzì, S. Roy
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Physiological Reports, Volume 14, Issue 9, May 2026.Abstract Glomerular podocytes play a key role in the pathogenesis of diabetic kidney disease (DKD). Recent studies suggest that natriuretic peptides (NPs) are podocyte protective. The beneficial effects of NPs are inhibited by the removal of NPs from the circulation by the NP clearance receptor (NPRC).
Liming Wang +4 more
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Solution regularity and smooth dependence for abstract equations and applications to hyperbolic PDEs [PDF]
, 2014 Irina Kmit, Lutz Recke
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Elliptic PDE learning is provably data-efficient. [PDF]
Proc Natl Acad Sci U S A, 2023 Boullé N, Halikias D, Townsend A.
europepmc +1 more source
Weak Galerkin finite element method for second order problems on curvilinear polytopal meshes with Lipschitz continuous edges or faces. [PDF]
Comput Math Appl, 2023 Guan Q, Queisser G, Zhao W.
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Anomalous Dissipation and Lack of Selection in the Obukhov-Corrsin Theory of Scalar Turbulence. [PDF]
Ann PDE, 2023 Colombo M, Crippa G, Sorella M.
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On the inverse problem of vibro-acoustography. [PDF]
Meccanica, 2023 Kaltenbacher B.
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Mathematical Foundations of Adaptive Isogeometric Analysis. [PDF]
Arch Comput Methods Eng, 2022 Buffa A +4 more
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On the Uniqueness of Schwarzschild-de Sitter Spacetime. [PDF]
Arch Ration Mech Anal, 2023 Borghini S, Chruściel PT, Mazzieri L.
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Mean-Field Limits: From Particle Descriptions to Macroscopic Equations. [PDF]
Arch Ration Mech Anal, 2021 Carrillo JA, Choi YP.
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