NUMERICAL EXPLORATION OF A FORWARD–BACKWARD DIFFUSION EQUATION

DOI10.1142/S0218202512500042zbMath1259.65129MaRDI QIDQ2911910

Corrado Mascia, Pauline Lafitte

Publication date: 3 September 2012

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

numerical resultsfinite difference methodphase transitionsnonlinear diffusion equationpropagation of transition interfacesthird-order PDE of pseudo-parabolic type

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Stefan problems, phase changes, etc. (80A22) Ill-posed problems for PDEs (35R25) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Ultraparabolic equations, pseudoparabolic equations, etc. (35K70) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30)

Related Items (10)

Backward parabolicity, cross-diffusion and Turing instability ⋮ The BGK approximation of kinetic models for traffic ⋮ Instability of Hysteretic Phase Interfaces in a Mean-Field Model with Inhomogeneities ⋮ Exponential stability of the traveling fronts for a viscous Fisher-KPP equation ⋮ A grid function formulation of a class of ill-posed parabolic equations ⋮ Hysteresis and phase transitions in a lattice regularization of an ill-posed forward-backward diffusion equation ⋮ Robust edge detector based on anisotropic diffusion-driven process ⋮ Two-phase entropy solutions of a forward-backward parabolic equation ⋮ Generalized transport model for phase transition with memory ⋮ Fast reaction limit and forward-backward diffusion: a Radon-Nikodym approach

Cites Work

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• HYPERBOLIC RELAXATION OF THE VISCOUS CAHN–HILLIARD EQUATION IN 3-D
• A posteriori error estimates with the finite element method of lines for a Sobolev equation
• Effect of aggregation on population recovery modeled by a forward-backward pseudoparabolic equation
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• A New Class of Entropy Solutions of the Buckley–Leverett Equation
• Long waves on a beach
• Pseudoparabolic Partial Differential Equations
• Model equations for long waves in nonlinear dispersive systems

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