Special Session 131: Recent progress on singularities formations of some evolution partial differential equations

Inhomogeneous exterior problems for the semilinear critical wave equationsCritical exponents for the quasilinear heat equations with combined nonlinearities

Berikbol T. Torebek
Ghent University
Belgium
Co-Author(s):    
Abstract:
This work studies the global behavior of solutions to the quasilinear inhomogeneous parabolic equation with combined nonlinearities. Firstly, we focus on an interesting phenomenon of discontinuity of the Fujita-type critical exponents. In particular, we will fill the gap in the results of Jleli-Samet-Souplet (Proc Am Math Soc 148:2579-2593, 2020) for the critical case. We are also interested in the influence of the forcing term on the critical behavior of the considered problem, so we will define the second critical exponent in the sense of Lee-Ni, depending on the forcing term.