Forced response of a linear hyperbolic system

Abstract

We study the forced response of a linear hyperbolic system of two equations in one spatial dimension and time. The characteristic directions are both negative and we examine an initial, boundary value problem in the first quadrant (t,x > 0) where one dependent variable is specified on the boundary x = 0 and an algebraic relationship exists between the two dependent variables along the initial time line. Special cases of the system arise in the investigation of small perturbations in the shock initiation of a dilute, chemically reacting fluid. A method of reflections is used to obtain explicit solutions and estimates for the long time, asymptotic approach to the steady state

Keywords:

• Hyperbolic system
• asymptotic solutions
• nonhomogeneous equations

AMS(MOS):

• 35L40
• 35B40
• 35L50

^∗Permanent Address: Dept. Of mathematics, University of Nebraska, Lincoln, Ne 68588-0323

^∗Permanent Address: Dept. Of mathematics, University of Nebraska, Lincoln, Ne 68588-0323

Notes

^∗Permanent Address: Dept. Of mathematics, University of Nebraska, Lincoln, Ne 68588-0323