Multi-dimension blow-up problem due to concentrated nonlinear source having local and nonlocal features

Abstract

This thesis studies a multi-dimensional parabolic problem with a concentrated nonlinear source having local and nonlocal fea¬tures. It is shown that there is a unique solution u before a blow-up occurs. A criterion for u to blow-up in a finite time is given. If u exists in a finite time only, then u blows up everywhere on the boundary of a ball where the concentrated local source is situated.