Long time existence for the heat equation with a noise term
type: Item
instance of: scholarly article
title: Long time existence for the heat equation with a noise term
zbMATH Open document ID: 0729.60055
DOI: 10.1007/BF01192141
publication date: 1991-01-01T00:00:00Z
review text: We consider the equation \(u_ t=u_{xx}+u^{\gamma}\dot W\) for x on a finite interval, with Dirichlet boundary conditions. \(\dot W\) is spacetime white noise. The initial condition is continuous and nonnegative. We show existence and uniqueness for all time, provided \(1\leq \gamma <3/2\).
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 4205534
zbMATH Keywords: two-parameter white noise
zbMATH Keywords: density of super-Brownian motion
zbMATH Keywords: Dirichlet boundary conditions
zbMATH Keywords: existence and uniqueness
author: Carl Mueller
MaRDI profile type: Publication
cites work: Super-Brownian motion: Path properties and hitting probabilities
cites work: Limit results for two stochastic partial differential equations
cites work: On the support of solutions to the heat equation with noise
cites work: Q3341599
cites work: Q3747436
cites work: Q4187050
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4205534