The Cauchy problem for Sobolev type equations

The talk is devoted to the Cauchy problem for linear Sobolev type equations with constant coefficients in a half-space in the class of generalized slow-growth functions. The necessary and sufficient condition for the uniqueness of the solution of the problem under consideration in the space of generalized slow-growth functions is indicated. Sufficient conditions for the existence of weak and strong generalized solutions of the Cauchy problem for various classes of linear equations of the Sobolev type in the space of generalized functions of slow growth are given.