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 $u_t+(b{u}^{k+1}{)}_x=u_{xx}$ in the case $b$ belongs to the Lorentz space $L^{p,\mathrm{\infty }}$.

This is a joint work with Stefano Bianchini.