Communications in Mathematical Analysis

Degenerate Abstract Parabolic Equations and Applications

Veli.B. Shakhmurov and Aida Sahmurova

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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.

Article information

Commun. Math. Anal., Volume 18, Number 2 (2015), 15-33.

First available in Project Euclid: 30 October 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35xx 47Fxx: Partial differential operators [See also 35Pxx, 58Jxx] 47Hxx: Nonlinear operators and their properties {For global and geometric aspects, see 49J53, 58-XX, especially 58Cxx} 35Pxx: Spectral theory and eigenvalue problems [See also 47Axx, 47Bxx, 47F05]

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


Shakhmurov, Veli.B.; Sahmurova, Aida. Degenerate Abstract Parabolic Equations and Applications. Commun. Math. Anal. 18 (2015), no. 2, 15--33.

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