A reaction-diffusion model for a class of nonlinear parabolic equations with moving boundaries: existence, uniqueness, exponential decay and simulation

DOI10.1016/j.apm.2014.04.045zbMath1449.35263OpenAlexW1983940803MaRDI QIDQ1634161

Y. Aharonov

Publication date: 17 December 2018

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2014.04.045

zbMATH Keywords

simulationmoving boundarystrong solutionmoving finite elementsnonlocal diffusion term

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Initial-boundary value problems for second-order parabolic equations (35K20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (10)

Semi-discrete finite-element approximation of nonlocal hyperbolic problem ⋮ Finite Element Scheme with Crank–Nicolson Method for Parabolic Nonlocal Problems Involving the Dirichlet Energy ⋮ On the finite element method for a nonlocal degenerate parabolic problem ⋮ L1 scheme on graded mesh for subdiffusion equation with nonlocal diffusion term ⋮ Stability estimate for a nonlinear coupled heat transfer model ⋮ On a nonlocal degenerate parabolic problem ⋮ Finite element schemes for a class of nonlocal parabolic systems with moving boundaries ⋮ Optimal error estimates of a linearized second-order BDF scheme for a nonlocal parabolic problem ⋮ Fully discrete finite element scheme for nonlocal parabolic problem involving the Dirichlet energy ⋮ Mesh-free Galerkin approximation for parabolic nonlocal problem using web-splines

Uses Software

• Matlab
• ode23
• ode45
• Ode15s
• ode113
• ode23s
• MATLAB ODE suite

Cites Work

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• On a class of problems involving a nonlocal operator.
• On global solvability and asymptotic behaviour of a mixed problem for a nonlinear degenerate Kirchhoff model in moving domains
• A moving finite element method for the solution of two-dimensional time-dependent models
• On weak solutions of a nonlinear hyperbolic-parabolic partial differential equation
• Existence and uniform decay for a nonlinear beam equation with nonlinearity of Kirchhoff type in domains with moving boundary
• The MATLAB ODE Suite
• Moving Finite Elements. II
• On hyperbolic–parabolic equations with nonlinearity of Kirchhoff–Carrier type in domains with moving boundary
• Some remarks on non local elliptic and parabolic problems

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