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

TL;DR

This paper establishes conditions under which nonlinear first-order hyperbolic systems with complex boundary conditions have globally smooth solutions, and identifies the nonlinearity thresholds that lead to solution blow-up.

Contribution

It provides new criteria for classical solvability of nonlinear hyperbolic systems with local and nonlocal boundary conditions and delineates the boundary between regular and singular solution behavior.

Findings

Proves global classical solvability under certain conditions.

Establishes lower bounds for nonlinearity leading to blow-up.

Identifies the frontier between regular and singular cases.

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).