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2015 Degenerate Abstract Parabolic Equations and Applications
Veli.B. Shakhmurov, Aida Sahmurova
Commun. Math. Anal. 18(2): 15-33 (2015).


Linear and nonlinear degenerate abstract parabolic equations with variable coefficients are studied. Here the equations and boundary conditions are degenerated on all boundary and contain some parameters. The linear problem is considered on the moving domain. The separability properties of elliptic and parabolic problems and Strichartz type estimates in mixed $L_{\mathbf{p}} $ 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.


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Veli.B. Shakhmurov. Aida Sahmurova. "Degenerate Abstract Parabolic Equations and Applications." Commun. Math. Anal. 18 (2) 15 - 33, 2015.


Published: 2015
First available in Project Euclid: 30 October 2015

zbMATH: 1327.35424
MathSciNet: MR3399819

Primary: 35PXX , 35XX , 47Fxx , 47Hxx

Keywords: degenerate PDE , differential-operator equations , nonlinear problems , positive operators in Banach spaces , semigroups of operators , separabile differential operators

Rights: Copyright © 2015 Mathematical Research Publishers

Vol.18 • No. 2 • 2015
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