Unbounded, periodic and almost periodic solutions of anisotropic parabolic equations with variable exponents of nonlinearity

Author
M. M. Bokalo
Ivan Franko National University of Lviv
Abstract
We prove the well-posedness of Fourier problems for anisotropic parabolic equations with variable exponents of nonlinearity without any assumptions on the solution behavior and growth of the initial data as time variable tends to minus infinity. We obtain estimates for generalized solutions of these problems as well as conditions for the existence of periodic and almost periodic solutions. Moreover, we prove some properties of the solutions of the problems under consideration.
Keywords
parabolic equation; Fourier problem; periodic solution; almost periodic solution
Reference
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Pages
81-91
Volume
41
Issue
1
Year
2014
Journal
Matematychni Studii
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