In present work studied the new boundary value problem for semi linear(Power-type nonlinearities)system equations of mixed hyperbolic-elliptic Keldysh type in the multivariate dimension with the changing time directio...In present work studied the new boundary value problem for semi linear(Power-type nonlinearities)system equations of mixed hyperbolic-elliptic Keldysh type in the multivariate dimension with the changing time direction.Considered problem and equation belongs to the modern level partial differential equations.Applying methods of functional analysis,topological methods,“ε”-regularizing.and continuation by the parameter at the same time with aid of a prior estimates,under assumptions conditions on coefficients of equations of system,the existence and uniqueness of generalized and regular solutions of a boundary problem are established in a weighted Sobolev's space.In this work one of main idea consists of show that the new boundary value problem which investigated in case of linear system equations can be well-posed when added nonlinear terms to this linear system equations,moreover in this case constructed new weithged spaces,the identity between of strong and weak solutions is established.展开更多
文摘In present work studied the new boundary value problem for semi linear(Power-type nonlinearities)system equations of mixed hyperbolic-elliptic Keldysh type in the multivariate dimension with the changing time direction.Considered problem and equation belongs to the modern level partial differential equations.Applying methods of functional analysis,topological methods,“ε”-regularizing.and continuation by the parameter at the same time with aid of a prior estimates,under assumptions conditions on coefficients of equations of system,the existence and uniqueness of generalized and regular solutions of a boundary problem are established in a weighted Sobolev's space.In this work one of main idea consists of show that the new boundary value problem which investigated in case of linear system equations can be well-posed when added nonlinear terms to this linear system equations,moreover in this case constructed new weithged spaces,the identity between of strong and weak solutions is established.