Special Session 123: Nonlinear phenomena in elliptic and parabolic equations

Uniform boundedness of solutions for superlinear heat equations
Yohei Fujishima
Shizuoka University
Japan
Co-Author(s):    Toru Kan
Abstract:
We study the $L^\infty$ estimates of radially symmetric solutions for a superlinear heat equation with the Dirichlet boundary condition, and show the uniform boundedness of global solutions. In particular, our results are applicable for nonlinear terms growing extremely faster than the exponential function when the space dimension is greater than 2 and smaller than 10.