Mixed problems for degenerate abstract parabolic equations and applications

Degenerate abstract parabolic equations with variable coefficients are studied. Here the boundary conditions are nonlocal. The maximal regularity properties of solutions for elliptic and parabolic problems and Strichartz type estimates in mixed Lebesgue spaces are obtained. Moreover, the existence a...

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Bibliographic Details
Published in:Carpathian Journal of Mathematics 2018-01, Vol.34 (2), p.247-254
Main Authors: Shakhmurov, Veli. B., Sahmurova, Aida
Format: Article
Language:English
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Summary:Degenerate abstract parabolic equations with variable coefficients are studied. Here the boundary conditions are nonlocal. The maximal regularity properties of solutions for elliptic and parabolic problems and Strichartz type estimates in mixed Lebesgue spaces are obtained. Moreover, the existence and uniqueness of optimal regular solution of mixed problem for nonlinear parabolic equation is established. Note that, these problems arise in fluid mechanics and environmental engineering.
ISSN:1584-2851
1843-4401
DOI:10.37193/CJM.2018.02.13