Well-posedness of parabolic equations containing hysteresis with diffusive thresholds

DOI10.1134/S0081543813080075zbMath1288.35277arXiv1411.0265OpenAlexW2032474439MaRDI QIDQ2446236

Dmitrii I. Rachinskii, Pavel L. Gurevich

Publication date: 16 April 2014

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.0265

zbMATH Keywords

long-term behaviorPreisach operatornon-ideal relay

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Initial-boundary value problems for second-order parabolic equations (35K20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Equations with nonlinear hysteresis operators (47J40) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (4)

Conditional uniqueness of solutions to the Keller-Rubinow model for Liesegang rings in the fast reaction limit ⋮ Periodic solutions to a class of biological diffusion models with hysteresis effect ⋮ Pattern formation in parabolic equations containing hysteresis with diffusive thresholds ⋮ Asymptotics of sign-changing patterns in hysteretic systems with diffusive thresholds

Cites Work

• Nonlinear diffusion equation and Liesegang rings
• Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis
• Global solutions of reaction-diffusion systems
• On well-posedness of the nonlocal boundary value problem for parabolic difference equations
• Evolution Problems with Hysteresis in the Source Term
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