Existence of solutions for degenerate parabolic equations with singular terms

Abstract

In this paper we deal with parabolic problems whose simplest model is $$\{\begin{array}{ll}{u}^{\prime }-{\Delta }_{p}u+B\frac{|\nabla u{|}^p}{u}=0& \text{in}(0,T)\times \Omega ,\\ u(0,x)=u_0(x)& \text{in}\Omega ,\\ u(t,x)=0& \text{on}(0,T)\times \partial \Omega ,\end{array}$$ where $T>0$, $N\ge 2$, $p>1$, $B>0$, and $u_0$ is a positive function in $L^{\infty }(\Omega )$ bounded away from zero.

References in corpus (3)

• Inverse Problem for a Curved Quantum Guide
• Existence and nonexistence of solutions for singular quadratic quasilinear equations
• Local estimates for parabolic equations with nonlinear gradient terms

Cited by in corpus (2)

• 1-Laplacian type problems with strongly singular nonlinearities and gradient terms
• Asymptotic behavior and existence of solutions for singular elliptic equations