Open AccessReaction-diffusion coupled inclusions with variable exponents and large diffusion
Author(s) -
Jacson Simsen,
Mariza Stefanello Simsen,
Petra Wittbold
Publication year - 2021
Publication title -
rocznik akademii górniczo-hutniczej im. stanisława staszica. opuscula mathematica/opuscula mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 16
eISSN - 2300-6919
pISSN - 1232-9274
DOI - 10.7494/opmath.2021.41.4.539
Subject(s) - mathematics , attractor , infinity , diffusion , mathematical analysis , differential inclusion , reaction–diffusion system , laplace operator , fractional laplacian , omega , physics , thermodynamics , quantum mechanics
This work concerns the study of asymptotic behavior of coupled systems of \(p(x)\)-Laplacian differential inclusions. We obtain that the generalized semiflow generated by the coupled system has a global attractor, we prove continuity of the solutions with respect to initial conditions and a triple of parameters and we prove upper semicontinuity of a family of global attractors for reaction-diffusion systems with spatially variable exponents when the exponents go to constants greater than 2 in the topology of \(L^{\infty}(\Omega)\) and the diffusion coefficients go to infinity.