Sahmurova, AidaShakhmurov, Veli B.2024-05-252024-05-25201311687-277010.1186/1687-2770-2013-302-s2.0-84888070771https://doi.org/10.1186/1687-2770-2013-30https://hdl.handle.net/20.500.14517/800The boundary value problems for singular degenerate arbitrary order differential-operator equations with variable coefficients are considered. The uniform coercivity properties of ordinary and partial differential equations with small parameters are derived in abstract spaces. It is shown that corresponding differential operators are positive and also are generators of analytic semigroups. In application, well-posedeness of the Cauchy problem for an abstract parabolic equation and systems of parabolic equations are studied in mixed spaces. These problems occur in fluid mechanics and environmental engineering. MSC: 34G10, 35J25, 35J70.eninfo:eu-repo/semantics/openAccessdifferential-operator equationsdegenerate equationssemigroups of operatorsBanach-valued function spacescoercive problemsoperator-valued Fourier multipliersinterpolation of Banach spacesArticleQ1Q2WOS:000316744200001