Existence and Blow-up for Non-Autonomous Scalar Conservation Laws With Viscosity

I will talk about the global existence/blow-up properties and the long-term behavior for the solutions of the scalar conservation law with viscosity $ u_t+(bu^{k+1})_x=u_{xx} $ in the case $ b $ belongs to the Lorentz space $ L^{p,\infty} $.

This is a joint work with Stefano Bianchini.