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.
We prove the Fredholm alternative for a class of two-dimensional firstorder hyperbolic systems with periodic-Dirichlet boundary conditions. Our approach is based on a regularization via a right parametrix.
We prove the Fredholm alternative for a class of two-dimensional firstorder hyperbolic systems with periodic-Dirichlet boundary conditions. Our approach is based on a regularization via a right parametrix.
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