| Abstract: |
| In this talk, I present a recent result on the initial-boundary value problem of a quasilinear elliptic-hyperbolic equation in one space dimension. A local-in-time weak solution to the problem is constructed by reformulating the problem as a partial differential inclusion and then appealing to the convex integration method through a sophisticated in-approximation scheme. In this way, the constructed solution exhibits a fine phase mixture in some space-time region on which the spatial derivative of the solution enters into the mixed elliptic-hyperbolic regime. I also add a numerical simulation through the FEM to show how such a solution can be well implemented. |
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