Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 305-312
Université Paris-Dauphine, CEREMADE, UMR CNRS 7534,
PSL Research university
Place du Maréchal de Lattre de Tassigny 75016 Paris, France;
clarkemove 'at' gmail.com
Universidade Estadual de Campinas,
Departamento de Matemática, IMECC
Campinas, Brazil;
colivera 'at' ime.unicamp.br
Abstract. We study the Lp-solutions for the semilinear heat equation with unbounded coefficients and driven by a infinite dimensional fractional Brownian motion with self-similarity parameter H > 1/2. Existence and uniqueness of local mild solutions are shown.
2010 Mathematics Subject Classification: Primary 60H15, 60H30, 35R60, 35K05, 35K10, 35K58.
Key words: Stochastic partial differential equation, heat equation, mild solution, fractional Brownian motion, cylindrical fractional Brownian motion, unbounded coefficients.
Reference to this article: J. Clarke and C. Olivera: Local Lp-solution for semilinear heat equation with fractional noise. Ann. Acad. Sci. Fenn. Math. 45 (2020), 305-312.
https://doi.org/10.5186/aasfm.2020.4505
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