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Amplitude Equation for SPDEs with Quadratic Non-Linearities


 
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1. Title Title of document Amplitude Equation for SPDEs with Quadratic Non-Linearities
 
2. Creator Author's name, affiliation, country Dirk Blömker; Universität Augsburg; Germany
 
2. Creator Author's name, affiliation, country Wael w mohammed; Universität Augsburg; Germany
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Amplitude equations, quadratic nonlinearities, separation of time- scales, SPDE
 
3. Subject Subject classification 60H15; 60H10, 35R60, 35Q99, 35K35.
 
4. Description Abstract In this paper we rigorously derive stochastic amplitude equations for a rather general class of SPDEs with quadratic nonlinearities forced by small additive noise. Near a change of stability we use the natural separation of time-scales to show that the solution of the original SPDE is approximated by the solution of an amplitude equation, which describes the evolution of dominant modes. Our results significantly improve older results. We focus on equations with quadratic nonlinearities and give applications to the one-dimensional Burgers’ equation and a model from surface growth.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) DFG (BL535/9-1), Long Term Mission system of the Egyptian government
 
7. Date (YYYY-MM-DD) 2009-11-13
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/716
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-716
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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