Stability in inverse source problems for nonlinear reaction-diffusion systems

DOI10.1007/s00030-021-00702-xzbMath1471.35337OpenAlexW3165960042MaRDI QIDQ2046643

Elena-Alexandra Melnig

Publication date: 26 August 2021

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-021-00702-x

zbMATH Keywords

reaction-diffusion systemsCarleman estimatessource estimates

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Inverse problems for PDEs (35R30) Observability (93B07) Initial-boundary value problems for second-order parabolic systems (35K51)

Cites Work

• An introduction to inverse elliptic and parabolic problems
• Entropy methods for reaction-diffusion equations: Slowly growing a-priori bounds
• Invariant sets and existence theorems for semilinear parabolic and elliptic systems
• Controllability of a \(4 \times 4\) quadratic reaction-diffusion system
• The Carleman inequality for linear parabolic equations in \(L^q\) norm.
• Exponential decay toward equilibrium via entropy methods for reaction-diffusion equations
• Stability in \(L^q\)-norm for inverse source parabolic problems
• Null Controllability of a Parabolic System with a Cubic Coupling Term
• A Maximum Principle for Semilinear Parabolic Systems
• Lipschitz stability in inverse parabolic problems by the Carleman estimate
• A strong maximum principle for parabolic systems in a convex set with arbitrary boundary
• Trend to Equilibrium for Reaction-Diffusion Systems Arising from Complex Balanced Chemical Reaction Networks
• Entropy, Duality, and Cross Diffusion
• Control of Three Heat Equations Coupled with Two Cubic Nonlinearities
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