Blow-up for a Porous Medium Equation with Local Linear Boundary Dissipation
Jichen YANG, Dengming Liu · Wuhan University Journal of Natural Sciences · 2024
This article investigates the blow-up behaviors for a porous medium equation with a superlinear source and local linear boundary dissipation. Making use of the concavity method, we establish sufficient conditions to guarantee the occurrence of the finite time blow-up phenomenon. Meanwhile, we show the existence of the finite time blow-up solutions for arbitrarily high initial energy. Finally, we derive the life span bounds (i.e., the lower and upper bounds of the blow-up time).