A constructive method for obtaining bounds on solutions of nonlinear hyperbolic problems

Abstract

Explicit upper and lower bounds are constructed for a functional defined on the difference of solutions to a class of nonlinear hyperbolic problems modelling string vibrations. Such bounds indicate how solutions are affected by the input data over a finite time interval. The logarithmic convexity method is used to obtain two second order ordinary differential inequalities for the appropriate functional. These inequalities are then related to two systems of first order equations whose solutions are the desired bounds.

AMS (MOS):

• 35B35
• 36L70
• 35R45