This MQP report concerns the finding of the convergence rates to the equilibrium constant states of shallow water wave equations with relaxation as time goes to infinity and establishing the existence of global in time solutions. We study the initial value problem, under a certain set of initial conditions, by considering the system in Lagrangian coordinates using different transformations. We develop two essential lemmas that we employ to prove the global in time existence of solutions and show, moreover, how these lemmas yield the convergence rates, given the initial conditions. We also look at the general case by strengthening the initial conditions and arrive at another system of equations that is similar to the previous one, the analysis of which follows naturally.
Worcester Polytechnic Institute
Electrical and Computer Engineering
Major Qualifying Project
All authors have granted to WPI a nonexclusive royalty-free license to distribute copies of the work, subject to other agreements. Copyright is held by the author or authors, with all rights reserved, unless otherwise noted.