Abstract
In this chapter we shall consider the solution \({Y }^{\varepsilon }\) of the SPDE (3.11), consisting of the deterministic Chafee–Infante equation perturbed by just the small jump part \({\xi }^{\varepsilon }\) of our Lévy process L.
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Notes
- 1.
As is usual when doing estimates for partial differential equations, the following computations are formal. They could be easily justified by first taking a smooth θ so that v is very regular and then approximating θ by a sequence of smooth functions.
References
A. Eden, C. Foias, B. Nicolaenko, R. Temam, Exponential Attractors for Dissipative Evolution Equations (Wiley/Massons, New York/Paris, 1994)
R. Temam, in Dynamical Systems in Physics and Applications. Springer Texts in Applied Mathematics (Springer, Berlin, 1992)
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Debussche, A., Högele, M., Imkeller, P. (2013). The Small Deviation of the Small Noise Solution. In: The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise. Lecture Notes in Mathematics, vol 2085. Springer, Cham. https://doi.org/10.1007/978-3-319-00828-8_4
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DOI: https://doi.org/10.1007/978-3-319-00828-8_4
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