Banach Journal of Mathematical Analysis

Linear and nonlinear degenerate abstract differential equations with small parameter

Veli B. Shakhmurov

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Abstract

The boundary value problems for linear and nonlinear regular degenerate abstract differential equations are studied. The equations have the principal variable coefficients and a small parameter. The linear problem is considered on a parameter-dependent domain (i.e., on a moving domain). The maximal regularity properties of linear problems and the optimal regularity of the nonlinear problem are obtained. In application, the well-posedness of the Cauchy problem for degenerate parabolic equations and boundary value problems for degenerate anisotropic differential equations are established.

Article information

Source
Banach J. Math. Anal., Volume 10, Number 1 (2016), 147-168.

Dates
Received: 2 February 2015
Accepted: 6 May 2015
First available in Project Euclid: 11 November 2015

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1447253826

Digital Object Identifier
doi:10.1215/17358787-3345071

Mathematical Reviews number (MathSciNet)
MR3453529

Zentralblatt MATH identifier
1335.35049

Subjects
Primary: 35J25: Boundary value problems for second-order elliptic equations
Secondary: 35B65: Smoothness and regularity of solutions 47N20: Applications to differential and integral equations

Keywords
differential equations semigroups of operators Banach-valued function spaces separable differential operators operator-valued Fourier multipliers

Citation

Shakhmurov, Veli B. Linear and nonlinear degenerate abstract differential equations with small parameter. Banach J. Math. Anal. 10 (2016), no. 1, 147--168. doi:10.1215/17358787-3345071. https://projecteuclid.org/euclid.bjma/1447253826


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