Existence And Uniqueness Results For A Class Of Nonlocal Conservation Laws By Means Of A Lax-Hopf-Type Solution Formula
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS(2020)
摘要
We study the initial value problem and the initial boundary value problem for nonlocal conservation laws. The nonlocal term is realized via a spatial integration of the solution between specified boundaries and affects the flux function of a given "local" conservation law in a multiplicative way. For a strictly convex flux function and strictly positive nonlocal impact we prove existence and uniqueness of weak entropy solutions relying on a fixed-point argument for the nonlocal term and an explicit Lax-Hopf-type solution formula for the corresponding Hamilton-Jacobi (HJ) equation. Using the developed theory for HJ equations, we obtain a semi-explicit Lax-Hopf-type formula for the solution of the corresponding nonlocal HJ equation and a semi-explicit Lax-Oleinik-type formula for the nonlocal conservation law.
更多查看译文
关键词
Conservation Laws, nonlocal conservation laws, Hamilton–, Jacobi equations, entropy conditions, Lax–, Oleinik formula
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要