Dovgay B. The properties of solutions of boundary-value problems of mathematical physics with random factors

There are found conditions of existence with probability one of twice continuously differentiated solutions of the boundary-value problems of mathematical physics for hyperbolic equation with random strictly phi-Sub-Gaussian right-hand side and zero initial and boundary conditions and for partial case of string oscillation equation with random right hand side which expressed through homogeneous strictly phi-Sub-Gaussian random field. The conditions of existence of generalized solution of hyperbolic equation with strictly phi-Sub-Gaussian random field in right-hand side are obtained. The estimations for distribution of supremum of solution of boundary-value problem of mathematical physics for hyperbolic equation with strictly phi-Sub-Gaussian random right-hand side are found. The obtained results are applied for construction of model of solution of hyperbolic equation with strictly phi-Sub-Gaussian random right-hand side and zero initial and boundary conditions which approximate this solution withgiven reliability and accuracy in uniform norm.