Nonlinear parabolic equations with nonstandard growth. Issue 12 (1st December 2016)

• Record Type: Journal Article
• Authors: Youssfi, A.; Azroul, E.; Lahmi, B.
• Is Part Of: Applicable analysis. Volume 95:Issue 12(2016)
• Page Start: 2766
• Page End: 2778
• Publication Date: 2016-12-01
• Subjects: Nonlinear parabolic equations -- variable exponents -- weak solutions; 35K55 -- 46E35 -- 35D30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1111999
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we study the solvability of the initial-boundary value problem for second-order nonlinear parabolic equations with nonstandard growth conditions and -source terms. In the model case, these equations include the p -Laplacian with a variable exponent p ( x, t ). We prove that if the variable exponent p is bounded away from both 1 and and is log-Hölder continuous, then the problem has a weak solution which satisfies the energy equality.