| Abstract: |
| We consider existence, uniqueness, and asymptotics of the porous medium equation in cones and half-spaces with homogeneous Dirichlet boundary conditions. We find that solutions depend quantitatively on the aperture of the cone via the first Dirichlet eigenvalue. Along the way, we prove the existence and uniqueness of dipole solutions in general cones, i.e. solutions that take as an initial datum a Dirac delta measure on the point of the cone. |
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