Some nonlinear stochastic Cauchy problems with generalized stochastic processes
type: Item
instance of: scholarly article
title: Some nonlinear stochastic Cauchy problems with generalized stochastic processes
zbMATH Open document ID: 1359.60078
DOI: 10.1155/2016/5963420
author: Victor Dévoué
published in: International Journal of Analysis
publication date: 2017-01-05T00:00:00Z
review text: Summary: We study some nonlinear stochastic Cauchy problems in the framework of the \((\mathcal{C}, \mathcal{E}, \mathcal{P})\)-algebras. We adapt the definitions to this framework. By means of suitable regularizations, we define associated generalized problems. We use our previous results about the wave equation in canonical form to obtain generalized solutions. We compare the generalized solutions with the classical ones when they exist.
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60G20
Mathematics Subject Classification ID: 35R60
zbMATH DE Number: 6670780
zbMATH Keywords: nonlinear stochastic Cauchy problems
zbMATH Keywords: generalized stochastic processes
zbMATH Keywords: regularizations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/5963420
OpenAlex ID: W2539398468
Wikidata QID: Q59123918
cites work: Fundamental structures and asymptotic microlocalization in sheaves of generalized functions
cites work: Well-posed problems in algebras of generalized functions
cites work: Q3314371
cites work: On generalized solutions to the wave equation in canonical form
cites work: Q3643393
cites work: Nonlinear stochastic wave equations
cites work: Q4815818
cites work: Q2752094
cites work: NONLINEAR STOCHASTIC WAVE EQUATION WITH COLOMBEAU GENERALIZED STOCHASTIC PROCESSES
cites work: Generalized Solutions to a Non Lipschitz-Cauchy Problem
description: scientific article; zbMATH DE number 6670780