High regularity of the solutions of the telegraph system subjected to nonlinear boundary conditions

Abstract

Some high regularity results are established for the solution of the nonlinear initial-boundary value problem (IBVP) (1.1)–(1.4) below. Using the characteristics of the corresponding linear homogeneous telegraph system (i.e., system (1.1)–(1.2) with F = 0 , f = 0 , G = 0 , and g = 0 ), we transform the original IBVP into a new one with linear homogeneous boundary conditions. This new equivalent problem is handled by using a semigroup approach as developed in [V.M. Hokkanen, G. Morosanu, Functional Methods in Differential Equations, Chapman & Hall/CRC, Boca Raton, FL, 2002].