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 global existence result for a (possibly sign changing) weak solution Cauchy–Dirichlet problem doubly nonlinear parabolic equations of form $$\begin{aligned} \partial _t\left( |u|^{q-1}u\right) -\Delta _p u=0\quad \text {in}\,\,\,\Omega _\infty , \end{aligned}$$ ∂ t | u q - 1 Δ p = 0 in Ω ∞ , where $$p>1$$ > $$q>0$$ . This is fair improvement preceding by authors (Nonlinear Anal 175C :157–172, 2018). The key tools employ are energy estimates approximate Rothe type integral strong convergence gradients solutions.