Local Well-posedness of A Non-local Burgers Equation

2013/09/16 by Hang Yang, Yang, Hang, Sam Goodchild +1 · 1 citation
Mathematics · Physics and Astronomy · Engineering · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1309.4128

Abstract

In this paper, we explore a nonlocal inviscid Burgers equation. Fixing a parameter h, we prove existence and uniqueness of the local solution of the equation \InviscidBurgersNonlocalu with periodic initial condition. We also explore the blow up properties of solutions to these kinds of equations with given periodic initial data, and show that there exists solutions that blow up in finite time and solutions that are globally regular. This contrasts with the classical inviscid Burgers equation, for which all non-constant smooth periodic initial data lead to finite time blow up. Finally, we present results of simulations to illustrate our findings.

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