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Subject: maximum principle × WGL Institute: WIAS ×

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Now showing 1 - 4 of 4
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    Global existence, uniqueness and stability for nonlinear dissipative systems of bulk-interface interaction
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Disser, Karoline
    We consider a general class of nonlinear parabolic systems corresponding to thermodynamically consistent gradient structure models of bulk-interface interaction. The setting includes non-smooth geometries and e.g. slow, fast and entropic diffusion processes under mass conservation. The main results are global well-posedness and exponential stability of equilibria. As a part of the proof, we show bulk-interface maximum principles and a bulk-interface Poincaré inequality. The method of proof for global existence is a simple but very versatile combination of maximal parabolic regularity of the linearization, a priori L1-bounds and a Schaefer fixed point argument. This allows us to extend the setting e.g. conditions and external forces.
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    Global-in-time existence of weak solutions to Kolmogorov's two-equation model of turbulence
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Mielke, Alexander; Naumann, Joachim
    We consider Kolmogorov's model for the turbulent motion of an incompressible fluid in 3. This model consists in a Navier-Stokes type system for the mean flow u and two further partial differential equations: an equation for the frequency and for the kinetic energy k each. We investigate this system of partial differential equations in a cylinder x ]0,T[ ( 3 cube, 0 < T < +∞) under spatial periodic boundary conditions on x ]0,T[ and initial conditions in x {0}. We present an existence result for a weak solution {u, , k} to the problem under consideration, with , k obeying the inequalities formula1 and formula2.
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    Forward-backward systems for expected utility maximization
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Horst, Ulrich
    In this paper we deal with the utility maximization problem with a general utility function. We derive a new approach in which we reduce the utility maximization problem with general utility to the study of a fully-coupled Forward-Backward Stochastic Differential Equation (FBSDE).
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    Positivity and time behavior of a general linear evolution system, non-local in space and time
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Khrabustovskyi, Andrii; Stephan, Holger
    We consider a general linear reaction-diffusion system in three dimensions and time, containing diffusion (local interaction), jumps (nonlocal interaction) and memory effects. We prove a maximum principle, and positivity of the solution, and investigate its asymptotic behavior. Moreover, we give an explicite expression of the limit of the solution for large times. In order to obtain these results we use the following method: We construct a Riemannian manifold with complicated microstructure depending on a small parameter. We study the asymptotic behavior of the solution of a simple diffusion equation on this manifold as the small parameter tends to zero. It turns out that the homogenized system coincides with the original reaction-diffusion system what allows us to investigate its properties.