In this paper, we study nonnegative and classical solutions u= u (x, t) u= u (x, t) to porous
medium problems of the type where Ω Ω is a bounded and smooth domain of R^ N RN, with …

In this paper, we apply positivity-preserving local discontinuous Galerkin (LDG) methods to
solve parabolic equations with blow-up solutions. This model is commonly used in …

This work is concerned with the development of a space-time adaptive numerical method,
based on a rigorous a posteriori error bound, for a semilinear convection-diffusion problem …

This paper concerns the study of the numerical approximation for the following
initialboundary value problem\left {u_t-u_ xx= f\left (u\right), x ∈\left (0, 1\right), t ∈\left (0 …

FULLY DISCRETE ADAPTIVE METHODS FOR A BLOW-UP PROBLEM 1. Introduction We are
interested in developing fully discrete adaptive nu Page 1 FULLY DISCRETE ADAPTIVE …

This work is devoted to the study of a posteriori error estimation and adaptivity in parabolic
problems with a particular focus on spatial discontinuous Galerkin (dG) discretisations. We …

We study numerical approximations to solutions of a system of two nonlinear diffusion
equations in a bounded interval, coupled at the boundary in a nonlinear way. In certain …

In this work, we study the numerical solution for parabolic equations whose solutions have a
common property of blowing up in finite time and the equations are invariant under the …

In this paper we present adaptive procedures for the numerical study of positive solutions of
the following problem: ut= uxx (x, t)∈(0, 1)×[0, T), ux (0, t)= 0 t∈[0, T), ux (1, t)= up (1, t) t∈[0 …

In this paper, we study the long-time behavior of nonnegative solutions of the heat equation
with a general memory boundary condition. We first present conditions on the memory term …