GLOBALATTRACTORFORANONLOCAL p -LAPLACEPARABOLIC EQUATION WITH NONLINEARITY OF ARBITRARY ORDER
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Tóm tắt
In this paper we consider a nonlocal p -Laplace parabolic equation depending on the Lp norm of the gradient with nonlinearity of arbitrary order. First, we prove the existence and uniqueness of weak solutions by combining the compactness and monotone methods and the weak convergence techniques in Orlicz spaces. Then, we prove the existence and regularity of a global attractor for the associated semigroup. The main novelty of our results is that no restriction on the upper growth of the nonlinearity is imposed.
Keywords: Nonlocal p -Laplace parabolic equation; nonlinearity of arbitrary order, weak solution, global attractor, compactness method, monotone method, weak convergence techniques.