THE CONSTRUCTION OF THE SOLUTIONS OF SOME PARTIAL-DIFFERENTIAL EQUATIONS

Differential equations of the form [GRAPHICS] are investigated in the regions [Ix[0, infinity)], where I is a certain interval of the real axis. The expressions P(ij)(D(t)) are differential polynomials with constant coefficients of the same order l for all i, j satifsying certain additional conditions. teh investigation is carried out using the methods of the operational calculus. Since no limitations are imposed on the behaviour of the functions u(x, t) as t --> + infinity, the operational calculus constructed by Mikusinskii is used without any connection with the Laplace transformation [1].