| Abstract: |
| We present new results on the Cahn-Hilliard equation on manifolds with conical singularities. We show how bounded imaginary powers and maximal regularity results obtained by Roidos and Schrohe can be used to prove that the solutions are globally defined in time and become instantaneously smooth in space and time. We use Mellin-Sobolev spaces to give precise information concerning the asymptotic behavior of the solutions close to the conical tips in terms of the local geometry. Finally we discuss some aspects of the dynamic behavior of the solutions on these spaces.
This a joint work with Nikolaos Roidos.
This work is partially supported by Funda\c{c}\~ao de Amparo \`a Pesquisa do Estado de S\~ao Paulo (FAPESP), Processo n\`umero: 2019/15200-1 |
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