Shakhmurov, Veli B.2024-05-252024-05-2520162662-20331735-878710.1215/17358787-33450712-s2.0-84955612848https://doi.org/10.1215/17358787-3345071https://hdl.handle.net/20.500.14517/185The 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.eninfo:eu-repo/semantics/openAccessdifferential equationssemigroups of operatorsBanach-valued function spacesseparable differential operatorsoperator-valued Fourier multipliersArticleQ2Q2101147168WOS:0003708141000104