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Well-posedness and long term behavior of supercritical wave equations driven by nonlinear colored noise on [formula omitted].
- Source :
-
Journal of Functional Analysis . Jul2022, Vol. 283 Issue 2, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
Abstract
- This paper is concerned with the well-posedness and long term behavior of the non-autonomous random wave equations driven by nonlinear colored noise on R n with n ≤ 5. The drift nonlinearity has a supercritical growth exponent (n + 2) / (n − 2). We first prove the existence and uniqueness of solutions in the energy space by showing the non-concentration of energy via the Morawetz identity and the uniform Strichartz estimates. We then prove the existence and uniqueness of tempered pullback random attractors of the non-autonomous random dynamical system associated with the equation. The asymptotic compactness of solutions is obtained by the idea of energy equation due to Ball and the uniform tail-ends estimates in order to circumvent the difficulty caused by the lack of compactness of Sobolev embeddings on unbounded domains. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00221236
- Volume :
- 283
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Functional Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 156649045
- Full Text :
- https://doi.org/10.1016/j.jfa.2022.109498