Drin Y. The Cauchy and nonlocal problems for parabolic pseudodifferential equations with nonsmooth symbols

Theory of correct solvability of nonlocal multi- time problem for evolutionary pseudodifferential equations (PDE) of finite and infinite order with PDO defined in different spaces of smooth functions. Been developed methodology survey FSCP, determined their structure and properties, showing the conditions of certainty the correct operator, where - PDO entire function of . Theorems of correct solbvability nonlocal multipoint time problem for evolutionary PDO with dot nonsmooth homogeneous and smooth character symbols when the limit function belongs to a class of distributions such as distributions. The solution of the Cauchy problem for quasilinear B-parabolic differential equations with deviation of the argument, and the solution of the Cauchy problem and the nonlocal problems for quasilinear pseudodifferential equations with deviation argument solved by steps. Investigated the direct and inverse problems for a class of evolution SDA method of incomplete separation of variables and using hybrid integrated Fourier space variables for classical and generalized by half-space variable.