Stability of Solutions to Generalized Forchheimer Equations of any Degree

L. Hoang, A. Ibragimov, T. Kieu, Z. Sobol

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

The dynamics of generalized Forchheimer equations for slightly compressible fluids are tudied by means of initial boundary value problem for the pressure. We prove that the solutions continuously depend on the boundary data and the Forchheimer polynomials. New bounds for the solutions are established in the Lα-norm for all α ≥ 1, and then are used to improve estimates for their spatial and time derivatives. New Poincaré–Sobolev inequalities and nonlinear Gronwall type estimates for nonlinear differential inequalities are utilized to achieve better asymptotic bounds. The methods developed can be applied to other degenerate parabolic equations. Bibliography: 25 titles.

Original languageEnglish
Pages (from-to)476-544
Number of pages69
JournalJournal of Mathematical Sciences (United States)
Volume210
Issue number4
DOIs
StatePublished - Oct 1 2015

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