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

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=0F=0, f=0f=0, G=0G=0, and g=0g=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].