| 2019年 11月18日（月）〜20日（水） |
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Michael Röckner 氏 （Universität Bielefeld）
Title:
Monotonicity methods for SPDE, including the time fractional case
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Abstract
In the first part of the lectures we shall give a concise overview on the theory and applications of SPDE with locally monotone coefficients under generalized growth and coercivity conditions. Applications include in particular classical cases as the stochastic 2D and 3D-Navier Stokes equations or the stochastic Cahn-Hilliard equation or surface growth models.
The second part will be devoted to the time fractional case. A general well-posedness result including the underlying main ideas and sketch of the proof will be presented. Applications here include the stochastic porous media, fast diffusion and p-Laplace equations with fractional time derivative.
The third lecture will be about a new approach to SPDE where solutions are constructed as zeros of maps on scaled spaces of random paths, which in the so-called "gradient case" turn out to be minimizers of appropriate convex functionals on such spaces.
講義時間
１８日：１０：３０〜１１：３０
１９日，２０日：１０：００〜１１：３０
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