Special Session 178: Nonlinear Evolution Equations and Related Topics

A doubly nonlinear parabolic equation with nonlinear perturbation under relaxed growth and exponent conditions
Shun Uchida
Oita University
Japan
Co-Author(s):    Shun Uchida
Abstract:
In this talk, we consider the initial boundary value problem for a doubly nonlinear parabolic equation with nonlinear perturbation, subject to homogeneous Dirichlet boundary conditions. Our main goal is to relax the growth conditions on the nonlinear term and to reduce the constraints on the exponent range, allowing the results to cover both singular and degenerate cases. The proof relies on an $L^{\infty}$-estimate for a time-discrete problem, obtained in earlier work, combined with the $L^{\infty}$-energy method.