Solutions for higher-order anisotropic elliptic-parabolic equations in time unbounded domains

• Main Authors: Mykola Bokalo, Iryna Skira
• Format: Article
• Language: English
• Published: BİSKA Bilisim Company 2018-03-01
• Series: New Trends in Mathematical Sciences
• Subjects: Fourier problem; elliptic-parabolic equation; periodic solution; Bohr almost periodic solutions; Stepanov almost periodic solutions.
• Online Access: https://ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=8418

The problem without initial conditions or, in other words, the Fourier problem for anisotropic elliptic-parabolic equations with variable exponents of nonlinearity in time unbounded domains is considered in this paper. The existence and uniqueness solutions of the problem are proved with no conditions on the behavior of solutions and growth of input data at infinity. The estimates of these solutions are received. In addition, some properties of the weak solutions of the Fourier problem are considered. The conditions for existence of periodic solutions of the considered equations are set. Also the conditions for existence of Bohr almost periodic solutions and Stepanov almost periodic solutions of some equations are obtained.