Abstract
Motivated by the work of Boulaaras and Haiour in [7], we provide a maximum norm analysis of Schwarz alternating method for parabolic p(x)-Laplacien equation, where an optimal error analysis each subdomain between the discrete Schwarz sequence and the continuous solution of the presented problem is established
Highlights
The constant α is assumed to be nonnegative satisfies f is a regular function such that α
According to Lipschitz assumption, they proved that for each subdomain an optimal error has been estimated by applying uniform norm between the discrete Schwarz sequence and the exact solution of a nonlinear parabolic partial differential equations
The same approach can be extended to other types as a linear parabolic partial differential equations see [2] and singularly perturbed advection-diffusion equations using the overlapping domain decomposition method, where we applied it in a full discrete
Summary
We consider the parabolic problem and transform it into elliptic system and give some definitions and classical results related to nonlinear elliptic equations with the function f is a regular and independent of the solution u. Where p− = min p(x) and p+ = max. Lp(·) = u : Ω → R measurable : |u(x)|p(x) dx. Parabolic p(x)-Laplacian Equation endowed with Luxembourg norm :. P(·)) is a reflexive Banach space, uniformly convex and its dual space is isomorphic to (Lp(·)(Ω), . Q(x)) where and W 1,p(x)(Ω) = {u ∈ Lp(x)(Ω), |∇u| ∈ Lp(x)(Ω)}, with the norm u = u p(x) + ∇u p(x), u ∈ W 1,p(x)(Ω). We denote by W01,p(x)(Ω) the closure of C0∞ in W 1,p(x)(Ω)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
