Abstract
In this paper, we explore a nonlocal inviscid Burgers’ equation. Fixing a parameter , we prove existence and uniqueness of the local solution of the equation with given periodic initial condition . We also explore the blow-up properties of the solutions to this Cauchy problem, and show that there exist initial data that lead to finite-time-blow-up solutions and others to globally regular solutions. This contrasts with the classical inviscid Burgers’ equation, for which all nonconstant smooth periodic initial data lead to finite-time blow-up. Finally, we present results of simulations to illustrate our findings.
Citation
Sam Goodchild. Hang Yang. "Local well-posedness of a nonlocal Burgers' equation." Involve 9 (1) 67 - 82, 2016. https://doi.org/10.2140/involve.2016.9.67
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