On the weak solution of a three‐point boundary value problem for a class of parabolic equations with energy specification | Zendy

Abdelfatah Bouziani | Zendy

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On the weak solution of a three‐point boundary value problem for a class of parabolic equations with energy specification

Author(s) -

Abdelfatah Bouziani

Publication year - 2003

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/s1085337503210010

Subject(s) - mathematics , uniqueness , sobolev space , mathematical analysis , boundary value problem , class (philosophy) , dirichlet problem , domain (mathematical analysis) , initial value problem , parabolic partial differential equation , weak solution , partial differential equation , artificial intelligence , computer science

This paper deals with weak solution in weighted Sobolev spaces, of three-point boundary value problems which combine Dirichlet and integral conditions, for linear and quasilinear parabolic equations in a domain with curved lateral boundaries. We, firstly, prove the existence, uniqueness, and continuous dependence of the solution for the linear equation. Next, analogous results are established for the quasilinear problem, using an iterative process based on results obtained for the linear problem

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