Solvability and Blow-up of Solutions of Semi Linear Parabolic Problem with Integral Condition of Second Type
by Saker Meriem   Oussaeif Taki-Eddine   Boumaza Nouri  

Vol. 15 No. 1 (2020) P.33~P.52

DOI:	https://doi.org/10.21915/BIMAS.2020103
	10.21915/BIMAS.2020103

ABSTRACT

In this paper, semi-linear parabolic equation with integral boundary condition of second type is investigated. The existence, uniqueness and Blow-up of weak solutions in finite time are established. The proof is proceeds in two steps; using the variable separation method for the solvability of the linear cas and applying an iterative process and a priori estimate, we prove the existence, uniqueness of the weak solution of the semi-linear problem. Finally, we study a blow-up of solution in finite time for a super-linear problem by using eigen functions method introduced by Kaplan.

KEYWORDS
Parabolic equation, semi linear parabolic eqautions, integral condition, blow-up of solution

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35K55, 35K61, 35B44, 35B45, 35A01, 35A02

MILESTONES

Received: 2020-01-21
Revised :
Accepted:

Download Full Content