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

2008/01/02 by Irina Kmit, Kmit, Irina
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.0801.0369

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).

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