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In this paper we are interested in the solvability of a mixed type Monge-Amp`ere equation, a homology equation appearing in a normal form theory of singular vector fields and the
—–, On a multidimensional problem of Goursat type for second order strictly hyperbolic systems.
It should be noted that the boundary value problem (1.6), (1.7) is a natural continuation of the known classical statements of the Goursat and Darboux problems (see, e.g., [1]–[3])
It is obvious that if the conditions of Theorem 2 are fulfilled, then the local solvability of problem (1), (2) guarantees its global solvability.. Therefore if the conditions
Degenerating hyperbolic equations, multidimensional ver- sions of a characteristic problem, Sobolev weighted space, functional space with negative
Formulation of the Problem and Main Results The Dirichlet problem for second order hyperbolic equations and some higher order linear hyperbolic equations with constant coefficients
The effective conditions guaranteeing the unique solvability of this problem and the stability of its solution with respect to small perturbations of the coefficients of the
SOLVABILITY AND THE UNIQUE SOLVABILITY OF A PERIODIC TYPE BOUNDARY VALUE PROBLEM FOR FIRST ORDER SCALAR FUNCTIONAL
