Quasilinear parabolic equations with p(x)-Laplacian diffusion terms and nonlocal boundary conditions

Abita Rahmoune, Benyattou Benabederrahmane


In this study, we prove the existence of local solution for a quasi linear generalized parabolic equation with nonlocal boundary conditions for an elliptic operator involving the variable-exponent nonlinearities, using Faedo-Galerkin arguments and compactness method.


Nonlocal boundary conditions; quasi-linear parabolic equations; Generalized Lebesgue space and Sobolev spaces with variable exponents

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URL http://www.elsevier.com/locate/na

DOI: http://dx.doi.org/10.24193/subbmath.2019.1.10