Degenerate parabolic equations appearing in atmospheric dispersion of pollutants

Veli Shakhmurov, Aida Sahmurova
2016 Electronic Journal of Qualitative Theory of Differential Equations  
Linear and nonlinear degenerate abstract parabolic equations with variable coefficients are studied. Here the equation 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 in mixed L p spaces are obtained. Moreover, the existence and uniqueness of optimal regular solution of mixed problem for nonlinear parabolic equation is established. Note that,
more » ... blished. Note that, these problems arise in fluid mechanics and environmental engineering. Keywords: differential-operator equations, degenerate PDE, semigroups of operators, nonlinear problems, separable differential operators, positive operators in Banach spaces.
doi:10.14232/ejqtde.2016.1.119 fatcat:y7iy53nvibahzdfkpyx7a5y5pe