Advances in Differential Equations
- Adv. Differential Equations
- Volume 19, Number 11/12 (2014), 997-1020.
Nonlocal $p$-Laplace equations depending on the $L^p$ norm of the gradient
We are studying a class of nonlinear nonlocal diffusion problems associated with a p-Laplace-type operator, where a nonlocal quantity is present in the diffusion coefficient. We address the issues of existence and uniqueness for the parabolic setting. Then, we study the asymptotic behavior of the solution for large time. For this purpose, we introduce and investigate, in detail, the associated stationary problem. Moreover, since the solutions of the stationary problem are also critical points of some energy functional, we make a classification of its critical points.
Adv. Differential Equations Volume 19, Number 11/12 (2014), 997-1020.
First available in Project Euclid: 18 August 2014
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35J60: Nonlinear elliptic equations 35K55: Nonlinear parabolic equations 35K92: Quasilinear parabolic equations with p-Laplacian 37B25: Lyapunov functions and stability; attractors, repellers
Chipot, Michel; Savitska, Tetiana. Nonlocal $p$-Laplace equations depending on the $L^p$ norm of the gradient. Adv. Differential Equations 19 (2014), no. 11/12, 997--1020. https://projecteuclid.org/euclid.ade/1408367286