Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

 Siegel der Universität Augsburg

 

Oberseminar Mathematische Modellierung und partielle Differentialgleichungen

 

Dr. Aleksandra Zimmermann
Universität Duisburg-Essen
 
spricht am
 
Dienstag, 8. Mai 2018
 
um
 
12:30 Uhr
 
im
 
Raum 2004 (L1)
 
über das Thema:
 

»Well-posedness for a class of nonlinear SPDEs with strongly continuous perturbation«

Abstract:
We consider the stochastic evolution equation du − div(a(x, u, Du) + F (u)) dt = Φ dW for T > 0, on a bounded Lipschitz domain D with homogeneous Dirichlet boundary conditions and initial condition in L2 (D). The main technical difficulties arise from the nonlinear diffusion-convection operator which is defined by a Carathéodory function a = a(x, λ, ξ) satisfying appropriate growth and coercivity assumptions and F : ℝ → ℝd Lipschitz continuous. On the right-hand side, we consider an additive stochastic perturbation with respect to a cylindrical Wiener process with values in L2 (D). We obtain approximate solutions by a semi-implicit time discretization. Adjusting the method of stochastic compactness to our setting, we are able to pass to the limit in the approximate equation. We show an L1-contraction principle and obtain existence and uniqueness of (stochastically) strong solutions.

 

Hierzu ergeht herzliche Einladung.
Prof. Dr. Lisa Beck


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