Existence and qualitative properties of a solution of the first mixed problem for a parabolic equation with non-power-law double nonlinearity (Q2812507)

This paper is concerned with qualitative properties of solutions to the first mixed problem of parabolic equations featuring double non-power-law nonlinearities in a cylindrical domain of the form \( D=\{t>0\}\times\Omega\), where the domain \( \Omega\subset \mathbb R^n\) is allowed to be unbounded. The existence of strong solutions is obtained by the method of Galerkin approximations in Sobolev-Orlicz spaces. A maximum principle is deduced along with upper and lower bounds characterizing the power-law decay of solution as \( t\to \infty\). Under certain hypotheses, uniqueness of the solution is also derived.