José C.M. Duque

Convergence of the Finite Element Method for the Porous Media Equation with Variable Exponent

In this work, we study the convergence of the finite element method when applied to the following parabolic equation:

The Euler-Galerkin finite element method for a nonlocal coupled system of reaction-diffusion type

u_t = div (|u| ^ {\gamma (\mathbf{x})} \nabla u) + f (\mathbf{x}, t)

Numerical study of the porous medium equation with absorption, variable exponents of nonlinearity and free boundary

,

Application of the moving mesh method to the porous medium equation with variable exponent

\mathbf{x}\in\Omega\subset R^{m}, t\in]0,T].

Discrete solutions for the porous medium equation with absorption and variable exponents

Since the problem may be of degenerate type, we utilize an approximate problem, regularized by introducing a parameter

On the finite element method for a nonlocal degenerate parabolic problem

\varepsilon

The Crank–Nicolson–Galerkin finite element method for a nonlocal parabolic equation with moving boundaries

. We prove, under certain conditions on

A reaction–diffusion model for the non-local coupled system: existence, uniqueness, long-time behaviour and localization properties of solutions

\gamma

On a nonlocal degenerate parabolic problem

and

Finite element schemes for a class of nonlocal parabolic systems with moving boundaries

f