On quasilinear parabolic equations in the Orlicz spaces
The paper under review deals with quasilinear parabolic equations of the form \[ \begin{cases} u_t-\text{div\,}\big(a(|\nabla u|)\nabla u\big)=g(u), & (x,t)\in \Omega\times(0,T),\\ u(x,t)=0, & (x,t)\in \partial\Omega\times(0,T),\\ u(x,0)=u_0(x)\in L^2(\Omega), & \end{cases} \] where \(\Omega\subset \mathbb{R}^n\) is a bounded and smooth domain. The authors study the existence and asymptotic behavior of solutions in the framework of the Orlicz-Sobolev spaces via operator theory and nonlinear semigroups theory.
scientific article; zbMATH DE number 6373715
scientific article