On the existence of weak solutions of nonlinear degenerate parabolic system with variable exponents. (1st January 2018)

• Record Type: Journal Article
• Authors: Shangerganesh, L.; Nyamoradi, N.; Deiva Mani, V.N.; Karthikeyan, S.
• Is Part Of: Computers & mathematics with applications. Volume 75:issue 1(2018)
• Page Start: 322
• Page End: 334
• Publication Date: 2018-01-01
• Subjects: Cancer invasion parabolic system -- Weak solution -- Faedo–Galerkin method; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.09.019
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: The main goal of the present paper is establishing the existence and uniqueness of weak solutions for the nonlinear degenerate reaction–diffusion system with variable exponents. A model also is proposed to characterize the invasion of cancer cells towards healthy cells with acidification environment. Moreover, the main results of this paper are obtained using regularization problem, the Faedo–Galerkin approximation method, some apriori estimates, compactness results and the Gronwall Lemma.