Regularity theory for elliptic and parabolic systems and problems in continuum mechanics

Telč, Czech Republic, 2.–5. 5. 2018

Program

To be announced.

Invited key lectures

Diego Cordóba

Shift of stability and mixing solutions for the Muskat problem

The Muskat equation governs the motion of an interface separation of two incompressible fluids in a porous media. In this talk I will present the following recent results: (1) The existence of solutions which shift stability regimes in the following sense: they start stable, then become unstable, and finally return back to the stable regime before it breaks down (joint work with J. Gomez-Serrano and A. Zlatos). (2) The existence of mixing solutions of the incompressible porous media equation for all Muskat type H^5 initial data in the fully unstable regime (joint work with A. Castro and D. Faraco).

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