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    STUDIA MATHEMATICA - Issue no. 1 / 2019  
         
  Article:   QUASILINEAR PARABOLIC EQUATIONS WITH p(x)-LAPLACIAN DIFFUSION TERMS AND NONLOCAL BOUNDARY CONDITIONS.

Authors:  ABITA RAHMOUNE, BENYATTOU BENABEDERRAHMANE.
 
       
         
  Abstract:  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.

Mathematics Subject Classifi cation (2010): 35K20, 35K59, 35B45, 35D30.
Keywords:
Nonlocal boundary conditions, quasi-linear parabolic equations,
generalized Lebesgue space and Sobolev spaces with variable exponents.
 
         
     
         
         
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