Quenching for a Diffusion System with Coupled Boundary Fluxes

Quenching for a Reaction-Diffusion System with Coupled Inner Singular Absorption Terms

we devote to investigate the quenching phenomenon for a reaction-diffusion system with coupled singular absorption terms, ut Δu − u−p1v−q1 , vt Δv − u−p2v−q2 . The solutions of the system quenches in finite time for any initial data are obtained, and the blow-up of time derivatives at the quenching point is verified. Moreover, under appropriate hypotheses, the criteria to identify the simultane...

Boundary Fluxes for Non-local Diffusion

Abstract. We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we l...

Quenching Time for a Nonlocal Diffusion Problem with Large Initial Data

The existence results for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions

In this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. The differential operator is taken in the Riemann-Liouville sense. Applying the Schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system D^{alpha}_{0+}x(t)=fleft(t,y(t),D^{p}_{0+}y(t)right), t in (0,...

Incomplete quenching in a system of heat equations coupled at the boundary

In this paper we find a possible continuation for quenching solutions to a system of heat equations coupled at the boundary condition. This system exhibits simultaneous and non-simultaneous quenching. For non-simultaneous quenching our continuation is a solution of a parabolic problem with Neumann boundary conditions. We also give some results for simultaneous quenching and present some numeric...