Existence and qualitative properties of a solution of the first mixed problem for a parabolic equation with non-power-law double nonlinearity. (11th March 2016)

• Record Type: Journal Article
• Authors: Andriyanova, È R; Mukminov, F Kh
• Is Part Of: Sbornik. Volume 207:Number 1(2016)
• Page Start: 1
• Page End: 40
• Publication Date: 2016-03-11
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM8484
• Languages: English
• ISSNs: 1064-5616

Abstract

Abstract: The first mixed problem is investigated for a certain class of parabolic equations with double non-power-law nonlinearities in a cylindrical domain of the form$ D=(t>0)\times\Omega$ . The domain$ \Omega\subset \mathbb R^n$ can be unbounded. The existence of strong solutions in a Sobolev-Orlicz space is proved by the method of Galerkin approximations. A maximum principle is established, and upper and lower bounds characterizing the power-law decay of solution as$ t\to \infty$ are proved. The uniqueness of the solution is proved under certain additional assumptions. Bibliography: 29 titles.