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Global attractor for a nonlocal p-Laplacian equation without uniqueness of solution

Partially funded by the projects MTM2015-63723-P (MINECO/FEDER, EU) and P12-FQM-1492 (Junta de Andalucía).
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  • In this paper, the existence of solution for a $p$ -Laplacian parabolic equation with nonlocal diffusion is established. To do this, we make use of a change of variable which transforms the original problem into a nonlocal one but with local diffusion. Since the uniqueness of solution is unknown, the asymptotic behaviour of the solutions is analysed in a multi-valued framework. Namely, the existence of the compact global attractor in $L^2(Ω)$ is ensured.

    Mathematics Subject Classification: Primary:35B41, 35K55, 35Q92, 37L30.


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