Classical Solution for Initial–Boundary Value Problem for Wave Equation with Integral Boundary Condition

Abstract

The unique existence of classical solution of initial–boundary value problem for wave equation with a special integral boundary condition is proved in the work. Classical solution of the problem in analytical form is also found in the article. This problem arises at the modeling of electromagnetic fields with arbitrary time dependence when interaction between the field and solids is simulated with impedance boundary conditions.

Keywords:

• initial–boundary value problem
• integral boundary condition
• characteristic method

AMS Subject Classification:

• 35G16
• 35L05