Bounds for functionals of solutions to a class of nonlinear hyperbolic equations

Abstract

Explicit upper and lower bounds are constructed for a functional defined on solutions to an initial-boundary value problem for the nonlinear equation u_tt=f(u_X)u_XX. These bounds are the solutions of two systems of first order ordinary differential equations which are obtained from two second order differential inequalities for the appropriate functional. The inequalities are derived using the logarithmic convexity method from ill posed problems.

AMS (MOS):

• 35B35
• 35L70
• 35R45