Existence of a Sign-Changing Weak Solution to Doubly Nonlinear Parabolic Equations
Existence of a Sign-Changing Weak Solution to Doubly Nonlinear Parabolic Equations
Abstract In this paper, assuming the initial-boundary datum belonging to suitable Sobolev and Lebesgue spaces, we prove the global existence result for a (possibly sign changing) weak solution to the Cauchy–Dirichlet problem for doubly nonlinear parabolic equations of the form $$\begin{aligned} \partial _t\left( |u|^{q-1}u\right) -\Delta _p u=0\quad \text {in}\,\,\,\Omega _\infty …