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Non-local diffusion equations involving the fractional \(p(\cdot)\)-Laplacian. (English) Zbl 1473.35350

In this work, the author study a class of nonlinear quasilinear diffusion equations involving the fractional \(p(\cdot)\)-Laplacian with variable exponents. Precisely, using techniques of monotone operators, the author established the well-posedness of solutions. He also study the large-time behaviour and extinction of solutions and he proved that the fractional \(p(\cdot)\)-Laplacian operator generates a (nonlinear) submarkovian semigroup on \(L^2(\Omega)\). In the last part of the paper he studied the existence of global attractors.

MSC:

35K92 Quasilinear parabolic equations with \(p\)-Laplacian
35R11 Fractional partial differential equations
35B40 Asymptotic behavior of solutions to PDEs
35K57 Reaction-diffusion equations
35K20 Initial-boundary value problems for second-order parabolic equations
35B41 Attractors
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