SBV regularity for Burgers-Poisson equation
Steven Gilmore, Khai T. Nguyen
TL;DR
This paper investigates the regularity properties of weak entropy solutions to the Burgers-Poisson equation, showing that their derivatives are composed solely of absolutely continuous and jump parts, indicating a specific structure of solutions.
Contribution
It establishes SBV regularity for solutions to the Burgers-Poisson equation, revealing the precise decomposition of their derivatives.
Findings
Derivatives of solutions have only absolutely continuous and jump parts.
SBV regularity is proven for weak entropy solutions.
The solution structure is clarified with respect to derivative decomposition.
Abstract
The SBV regularity of weak entropy solutions to the Burgers-Poisson equation is considered. We show that the derivative of a solution consists of only the absolutely continuous part and the jump part.
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