On the Burgers-Poisson Equation
Katrin Grunert, Khai T. Nguyen
TL;DR
This paper establishes the existence, uniqueness, and certain regularity properties of weak entropy solutions to the Burgers-Poisson equation, including criteria for smoothness and wave breaking.
Contribution
It provides the first rigorous proof of existence and uniqueness of weak entropy solutions for the Burgers-Poisson equation with L^1 initial data, along with regularity criteria.
Findings
Proved existence and uniqueness of solutions
Established Oleinik type estimate
Provided criteria for wave breaking
Abstract
In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L^1(R). Additional an Oleinik type estimate is established and some criteria on local smoothness and wave breaking for weak entropy solutions are provided.
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