Equivalence between radial solutions of different parabolic gradient-diffusion equations and applications
| Autor: | Juan Luis Vázquez, Mikko Parviainen |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
010102 general mathematics
Mathematical analysis Space dimension Stochastic game Mathematics::Analysis of PDEs 01 natural sciences Theoretical Computer Science 010101 applied mathematics Mathematics - Analysis of PDEs Mathematics (miscellaneous) Bounded function FOS: Mathematics Initial value problem 0101 mathematics 35K55 49L25 35B40 35K65 35K67 Equivalence (measure theory) Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE. :303-359 |
| ISSN: | 2036-2145 0391-173X |
| Popis: | We consider a general form of a parabolic equation that generalizes both the standard parabolic $p$-Laplace equation and the normalized version that has been proposed in stochastic game theory. We establish an equivalence between this equation and the standard $p$-parabolic equation posed in a fictitious space dimension, valid for radially symmetric solutions. This allows us to find suitable explicit solutions for example of Barenblatt type, and as a consequence we settle the exact asymptotic behaviour of the Cauchy problem even for nonradial data. We also establish the asymptotic behaviour in a bounded domain. Moreover, we use the explicit solutions to establish the parabolic Harnack's inequality. |
| Databáze: | OpenAIRE |
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