Title: Classical solvability of nonlinear initial-boundary problems for first-order hyperbolic systems

Authors: Irina Kmit

Addresses: Institute for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, Naukova St. 3b, Lviv 79060, Ukraine

Abstract: We prove the global classical solvability of initial-boundary problems for semilinear first-order hyperbolic systems subjected to local and nonlocal nonlinear boundary conditions. We also establish lower bounds for the order of nonlinearity demarkating a frontier between regular cases (classical solvability) and singular cases (blow-up of solutions).

Keywords: first-order hyperbolic systems; nonlinear boundary conditions; non-Lipschitz nonlinearities; classical solvability.

DOI: 10.1504/IJDSDE.2008.019680

International Journal of Dynamical Systems and Differential Equations, 2008 Vol.1 No.3, pp.191 - 195

Published online: 20 Jul 2008 *

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