Optimal regularity in time and space for the porous medium equation
| Autor: | Benjamin Gess, Eitan Tadmor, Jonas Sauer |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
velocity
35D30 Scale (ratio) regularity results 01 natural sciences Mathematics - Analysis of PDEs porous medium equation 0103 physical sciences kinetic formulation FOS: Mathematics Limit (mathematics) 0101 mathematics Scaling entropy solutions Mathematics averaging Numerical Analysis 35K59 35B65 35D30 76SXX 35B65 Spacetime Applied Mathematics 010102 general mathematics Mathematical analysis velocity averaging Sobolev space 35K59 010307 mathematical physics Porous medium Analysis Analysis of PDEs (math.AP) 76S05 |
| Zdroj: | Anal. PDE 13, no. 8 (2020), 2441-2480 |
| Popis: | Regularity estimates in time and space for solutions to the porous medium equation are shown in the scale of Sobolev spaces. In addition, higher spatial regularity for powers of the solutions is obtained. Scaling arguments indicate that these estimates are optimal. In the linear limit, the proven regularity estimates are consistent with the optimal regularity of the linear case. 36 pages |
| Databáze: | OpenAIRE |
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