Dynamics of propagation and interaction of \(\delta\)-shock waves in conservation law systems
The authors consider the system of conservation laws \[ u_t+(F(u,v))_x=0, \quad v_t+(G(u,v))_x=0, \] where the real functions \(F(u,v)\) and \(G(u,v)\) are smooth with respect to their arguments and linear in \(v\). Here \(u=u(x,t)\in \mathbb R \) and \(v=v(x,t)\in \mathbb R \) are unknown functions which depend on real arguments. A new definition of a \(\delta \)-shock wave type solution for the system under consideration is introduced. The authors establish a new weak asymptotics method by which they construct formulas describing the propagation and interaction of \(\delta \)-shock waves. The merging of two \(\delta \)-shock waves is discussed as well.
scientific article; zbMATH DE number 2164779
scientific article