Universidad Complutense de Madrid
E-Prints Complutense

The extinction versus the blow-up: Global and non-global existence of solutions of source types of degenerate parabolic equations with a singular absorption.

Impacto

Downloads

Downloads per month over past year

Dao, A. N and Díaz Díaz, Jesús Ildefonso (2017) The extinction versus the blow-up: Global and non-global existence of solutions of source types of degenerate parabolic equations with a singular absorption. Journal of Differential Equations, 263 (10). pp. 6764-6804. ISSN 0022-0396

[img] PDF
Restringido a Repository staff only

1MB

Official URL: http://www.sciencedirect.com/science/article/pii/S0022039617303844


URLURL Type
http://www.sciencedirect.com/Publisher


Abstract

We consider nonnegative solutions of degenerate parabolic equations with a singular absorption term and a source nonlinear term: partial derivative(t)u - (vertical bar u(x)vertical bar(P-2)u(x))(x) + u(-beta) X{u > 0} = f (u,x,t), in I x (0, T), with the homogeneous zero boundary condition on I = (x(1), x(2)), an open bounded interval in R. Through this paper, we assume that p > 2 and beta is an element of (0, 1). To show the local existence result, we prove first a sharp pointwise estimate for vertical bar u(x vertical bar) I. One of our main goals is to analyze conditions on which local solutions can be extended to the whole time interval t is an element of(0, infinity), the so called global solutions, or by the contrary a finite time blow-up tau(0) > 0 arises such that lim (t ->tau 0) vertical bar vertical bar u(t)vertical bar vertical bar(L infinity(I)) = +infinity. Moreover, we prove that any global solution must vanish identically after a finite time if provided that either the initial data or the source term is small enough. Finally, we show that the condition f (0, x, t) = 0, for all(x, t) is an element of I x (0, infinity) is a necessary and sufficient condition for the existence of solution of equations of this type.


Item Type:Article
Uncontrolled Keywords:Degenerate parabolic equations; Gradient estimates; Extinction; Global existence; Blow-up
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:45117
Deposited On:18 Oct 2017 09:42
Last Modified:12 Dec 2018 15:06

Origin of downloads

Repository Staff Only: item control page