Well-posedness of boundary-value problems for multidimensional hyperbolic systems

Abstract

517.95By using the method of characteristics, we investigate the well-posedness of local problems (Cauchy problem and mixed problems) and nonlocal problems (with nonseparable and integral conditions) for some multidimensional almost-linear hyperbolic systems of the first order. We reduce these problems to systems of integro-operator equations and prove theorems on the existence and uniqueness of classical solutions.