On Asymptotic Variational Wave Equations

Alberto Bressan, Ping Zhang, Yuxi Zheng

We investigate the equation $(u_t+(f(u){)}_x{)}_x=f^{\prime \prime }(u)(u_x{)}^2/2$ where $f(u)$ is a given smooth function. Typically $f(u)=u^2/2$ or $u^3/3$. This equation models unidirectional…