Blow-Up Solution of a Porous Medium Equation with Nonlocal Boundary Conditions

Abstract EN

In this paper, we devote to studying the blow-up phenomena for a porous medium equation under nonlocal boundary conditions.

Based on auxiliary functions and differential inequality technique, we derive the sufficient conditions to guarantee the existence of blow-up solutions under different measures and obtain an upper bound for blow-up time.

Moreover, we demonstrate the lower bounds for blow-up time under some appropriate measures in R3 and in the higher-dimensional space Rnn≥3, respectively.

At last, two examples are given to illustrate the applications of main results.