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.
Keywords
nonlocal Burgers' equation, finite-time blow-up, global
regularity