Weak solutions of fractional differential equations in non cylindrical domains. (August 2017)

• Record Type: Journal Article
• Authors: Kubica, A.; Rybka, P.; Ryszewska, K.
• Is Part Of: Nonlinear analysis. Volume 36(2017)
• Page Start: 154
• Page End: 182
• Publication Date: 2017-08
• Subjects: Time fractional Caputo derivative -- Heat equation -- Galerkin method; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.01.005
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We study a time fractional heat equation in a non cylindrical domain. The problem is one-dimensional. We prove existence of properly defined weak solutions by means of the Galerkin approximation. Highlights: A time fractional diffusion equation in non cylindrical domains is studied. The Galerkin method is used to obtain a weak solution. Special approximate solutions are defined to obtain a priori estimates. A notion of a weak solution is worked out.