Weak exponential attractors for Coleman-Gurtin equations with dynamic boundary conditions possessing different memory kernels

DOI10.12775/TMNA.2019.095zbMath1439.35083arXiv1910.00396WikidataQ115516317 ScholiaQ115516317MaRDI QIDQ2179282

Joseph L. Shomberg

Publication date: 12 May 2020

Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.00396

zbMATH Keywords

memory relaxationsingularly perturbed memory kernels

Mathematics Subject Classification ID

Attractors (35B41) Integro-partial differential equations (45K05) Semilinear parabolic equations (35K58) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61) PDEs in connection with classical thermodynamics and heat transfer (35Q79)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Singular limit of viscous Cahn-Hilliard equations with memory and dynamic boundary conditions
• Robust exponential attractors for a family of nonconserved phase-field systems with memory
• Asymptotics of the Coleman-Gurtin model
• Well posedness and the global attractor of some quasi-linear parabolic equations with nonlinear dynamic boundary conditions.
• Robust exponential attractors for non-autonomous equations with memory
• Weakly dissipative semilinear equations of viscoelasticity
• Phase-field systems with nonlinear coupling and dynamic boundary conditions
• Robust exponential attractors for a phase-field system with memory
• Singular limit of dissipative hyperbolic equations with memory
• Global well-posedness for the non-isothermal Cahn-Hilliard equation with dynamic boundary conditions
• The non-isothermal Allen-Cahn equation with dynamic boundary conditions
• The Caginalp phase-field system with coupled dynamic boundary conditions and singular potentials
• Robust exponential attractors for the strongly damped wave equation with memory. II.
• Semigroups of linear operators and applications to partial differential equations
• Infinite-dimensional dynamical systems in mechanics and physics
• Asymptotic behavior of a semilinear problem in heat conduction with memory
• On the damped semilinear wave equation with critical exponent
• Uniform exponential attractors for a singularly perturbed damped wave equation.
• Coleman-Gurtin type equations with dynamic boundary conditions
• Thermodynamics and departures from Fourier's law of heat conduction
• Attractors for the Cahn-Hilliard equation with memory in 2D
• Robust Exponential Attractors for Coleman--Gurtin Equations with Dynamic Boundary Conditions Possessing Memory
• Attractors for strongly damped wave equations with nonlinear hyperbolic dynamic boundary conditions
• Continuous families of exponential attractors for singularly perturbed equations with memory
• Uniform attractors for a non-autonomous semilinear heat equation with memory
• Exponential attractors for a nonlinear reaction-diffusion system in
• Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions
• Hyperbolic relaxation of reaction-diffusion equations with dynamic boundary conditions
• Singular limit of differential systems with memory
• Global and exponential attractors for 3‐D wave equations with displacement dependent damping
• A construction of a robust family of exponential attractors
• Nonlinear balance for reaction-diffusion equations under nonlinear boundary conditions: Dissipativity and blow-up