Quenching Phenomena Due to a Concentrated Nonlinear Source in an Infinitely Long Cylinder

Abstract

This article studies a semilinear parabolic first initial-boundary value problem with a concentrated nonlinear source in an infinitely long cylinder. We study the effects of the strength of the source on quenching. Criteria for global existence of the solution and for quenching are investigated.

On the existence of weak solutions for a class of singular reaction diffusion systems

“…This is due to its many and varied applications in the fields of science, especially engineering. We find a lot of models in Constantin et al [6], Kiselev and Zlatos [16] and Marion [22]. For example, quenching can increase the hardness of metallic or plastic materials, to see other examples we refer to Aris [3], Muntean [26] and references given there.…”

“…In this work, we are interested in the study of a singular reaction diffusion system. For modeling and mathematical analysis of this type of problem, several methods have been proposed; see for example, [1,2], [4], [5], [7], [9][10][11][12][13][14], [21][22][23][24], [29][30][31][32][33], [37] and corresponding references therein.…”