| Abstract: |
| We consider one-dimensional problems (P) for scalar parabolic-hyperbolic conservation laws. These equations may be regarded as a combination of scalar hyperbolic conservation laws and porous medium type equations. Hence, they have both properties of hyperbolic equations and those of parabolic equations.
In this talk, we study qualitative properties of entropy solutions to (P). In particular, we focus on the free boundary separating the parabolic and hyperbolic regions.
We first review our previous results on the construction of traveling waves, one-sided Lipschitz estimates and decay estimates for entropy solutions. We then investigate the behavior of the free boundary, drawing on propagation estimates for the support of solutions to the porous medium equation and estimates for the interface of the mushy region in the enthalpy formulation of the Stefan problem. |
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