Communications in Mathematical Analysis

Degenerate Abstract Parabolic Equations and Applications

Veli.B. Shakhmurov and Aida Sahmurova

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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

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

Dates
First available in Project Euclid: 30 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.cma/1446210171

Mathematical Reviews number (MathSciNet)
MR3399819

Zentralblatt MATH identifier
1327.35424

Subjects
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]

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

Citation

Shakhmurov, Veli.B.; Sahmurova, Aida. Degenerate Abstract Parabolic Equations and Applications. Commun. Math. Anal. 18 (2015), no. 2, 15--33. https://projecteuclid.org/euclid.cma/1446210171


Export citation