Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 10, Number 1 (2016), 147-168.
Linear and nonlinear degenerate abstract differential equations with small parameter
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.
Banach J. Math. Anal., Volume 10, Number 1 (2016), 147-168.
Received: 2 February 2015
Accepted: 6 May 2015
First available in Project Euclid: 11 November 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35J25: Boundary value problems for second-order elliptic equations
Secondary: 35B65: Smoothness and regularity of solutions 47N20: Applications to differential and integral equations
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