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

2019 ◽  
Vol 64 (1) ◽  
pp. 103-118
Author(s):  
Abita Rahmoune ◽  
◽  
Benyattou Benabderrahmane ◽  
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Quasilinear Parabolic Equations ◽  
Quasilinear Parabolic

scholarly journals On the solvability of a class of singular parabolic equations with nonlocal boundary conditions in nonclassical function spaces

2002 ◽  
Vol 30 (7) ◽  
pp. 435-447 ◽  
Author(s):  
Abdelfatah Bouziani
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
A Priori ◽  
Nonlocal Boundary ◽  
A Priori Estimate ◽  
Nonlocal Boundary Conditions ◽  
Generalized Solution ◽  
Function Spaces ◽  
Singular Parabolic Equations ◽  
Abstract Formulation

The aim of this paper is to prove the existence, uniqueness, and continuous dependence upon the data of a generalized solution for certain singular parabolic equations with initial and nonlocal boundary conditions. The proof is based on an a priori estimate established in nonclassical function spaces, and on the density of the range of the operator corresponding to the abstract formulation of the considered problem.

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