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Multi angle
Asymptotics for some non-linear stochastic heat equations
Auteurs : Nualart, Eulalia (Auteur de la Conférence)
CIRM (Editeur )
CIRM (Editeur )
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Résumé :
Consider the following stochastic heat equation,
\[
\frac{\partial u_t(x)}{\partial t}=-\nu(-\Delta)^{\alpha/2} u_t(x)+\sigma(u_t(x))\dot{F}(t,\,x), \quad t>0, \; x \in \mathbb{R}^d.
\]
Here $-\nu(-\Delta)^{\alpha/2}$ is the fractional Laplacian with $\nu>0$ and $\alpha \in (0,2]$, $\sigma: \mathbb{R}\rightarrow \mathbb{R}$ is a globally Lipschitz function, and $\dot{F}(t,\,x)$ is a Gaussian noise which is white in time and colored in space. Under some suitable conditions, we will explore the effect of the initial data on the spatial asymptotic properties of the solution. We also prove a strong comparison principle thus filling an important gap in the literature.
Joint work with Mohammud Foondun (University of Strathclyde).
Codes MSC : \[
\frac{\partial u_t(x)}{\partial t}=-\nu(-\Delta)^{\alpha/2} u_t(x)+\sigma(u_t(x))\dot{F}(t,\,x), \quad t>0, \; x \in \mathbb{R}^d.
\]
Here $-\nu(-\Delta)^{\alpha/2}$ is the fractional Laplacian with $\nu>0$ and $\alpha \in (0,2]$, $\sigma: \mathbb{R}\rightarrow \mathbb{R}$ is a globally Lipschitz function, and $\dot{F}(t,\,x)$ is a Gaussian noise which is white in time and colored in space. Under some suitable conditions, we will explore the effect of the initial data on the spatial asymptotic properties of the solution. We also prove a strong comparison principle thus filling an important gap in the literature.
Joint work with Mohammud Foondun (University of Strathclyde).
35R60 - PDEs with randomness, stochastic PDE
60H15 - Stochastic partial differential equations
60J55 - Local time and additive functionals
Ressources complémentaires :
https://www.cirm-math.fr/ProgWeebly/Renc1742/Nualart.pdf
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Informations sur la Vidéo
Langue : AnglaisDate de publication : 22/05/2018 Date de captation : 16/05/2018 Collection : Partial Differential Equations ; Probability and Statistics Sous collection : Research talks Format : MP4 Domaine : Probability & Statistics ; PDE Durée : 00:39:30 Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2018-05-16_Nualart.mp4 
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Informations sur la rencontre
Nom de la rencontre : Stochastic partial differential equations / Equations aux dérivées partielles stochastiquesOrganisateurs de la rencontre : Berglund, Nils ; Debussche, Arnaud ; Delarue, François ; Kuehn, Christian Dates : 14/05/2018 - 18/05/2018 Année de la rencontre : 2018 URL Congrès : https://conferences.cirm-math.fr/1742.html Citation Data
DOI : 10.24350/CIRM.V.19402003Cite this video as: Nualart, Eulalia (2018). Asymptotics for some non-linear stochastic heat equations. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19402003 URI : http://dx.doi.org/10.24350/CIRM.V.19402003 |
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