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Strong solutions of semilinear stochastic partial differential equations |
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| Authors: | Martina Hofmanová |
| Affiliation: | 1. Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic 2. Institute of Information Theory and Automation of the ASCR, Pod Vodárenskou vě?í 4, 182 08, Praha 8, Czech Republic 3. IRMAR, ENS Cachan Bretagne, CNRS, UEB av. Robert Schuman, 35 170, Bruz, France |
| Abstract: | We study the Cauchy problem for a semilinear stochastic partial differential equation driven by a finite-dimensional Wiener process. In particular, under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives, we consider the equation in the context of power scale generated by a strongly elliptic differential operator. Application of semigroup arguments then yields the existence of a continuous strong solution. |
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