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Local Well-posedness of A Non-local Burgers Equation by Yang, Hang; Goodchild, Sam is a scholarly article available to read on EtoBox.

What is Local Well-posedness of A Non-local Burgers Equation about?

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 $\InviscidBurgersNonlocal{u}$ 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.

Author

Yang, Hang; Goodchild, Sam

Published

2013

Language

EN