Blow-up of the solution for a singular semilinear parabolic problem due to a concentrated nonlinear source
by
J. C. Carrillo-Escobar
Department of Mathematics, University of Louisiana at Lafayette, Lafayette LA 70504-1010 USA
Coauthors: C. Y. Chan, Department of Mathematics, University of Louisiana at Lafayette, Lafayette LA 70504-1010 USA

Let a, T and r be real numbers such that a and T are positive and r < 1. We study the following singular semilinear parabolic first initial-boundary value problem,

ut - uxx -  r x  ux  =  ad(x-b)f(u(x, t))  for  0 < x < 1,  0 < t ≤ T,

u(x, 0)  =  y(x)   for  0 ≤ x ≤ 1,   u(0, t)  =  0   =  u(1, t)   for  0 < t ≤ T,

where d(x) is the Delta Dirac function and f and y are given function. Existence, uniqueness and the blow-up of u are investigated.

Date received: March 28, 2007