Publikation: Center manifolds for rough partial differential equations
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2023
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Kuehn, Christian
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Electronic Journal of Probability. Institute of Mathematical Statistics (IMS). 2023, 28, 48. eISSN 1083-6489. Available under: doi: 10.1214/23-ejp938
Zusammenfassung
We prove a center manifold theorem for rough partial differential equations (rough PDEs). The class of rough PDEs we consider contains as a key subclass reaction-diffusion equations driven by nonlinear multiplicative noise, where the stochastic forcing is given by a γ-Hölder rough path, for γ∈(1∕3,1∕2]. Our proof technique relies upon the theory of rough paths and analytic semigroups in combination with a discretized Lyapunov-Perron-type method in a suitable scale of interpolation spaces. The resulting center manifold is a random manifold in the sense of the theory of random dynamical systems (RDS). We also illustrate our main theorem for reaction-diffusion equations as well as for the Swift-Hohenberg equation.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
center manifold, rough path, evolution equation, interpolation spaces, Lyapunov- Perron method
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KUEHN, Christian, Alexandra BLESSING-NEAMTU, 2023. Center manifolds for rough partial differential equations. In: Electronic Journal of Probability. Institute of Mathematical Statistics (IMS). 2023, 28, 48. eISSN 1083-6489. Available under: doi: 10.1214/23-ejp938BibTex
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title={Center manifolds for rough partial differential equations},
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author={Kuehn, Christian and Blessing-Neamtu, Alexandra},
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