Zobrazeno 1 - 10
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pro vyhledávání: '"Zinsl, Jonathan"'
Autor:
Matthes, Daniel, Zinsl, Jonathan
This article is concerned with the existence and the long time behavior of weak solutions to certain coupled systems of fourth-order degenerate parabolic equations of gradient flow type. The underlying metric is a Wasserstein-like transportation dist
Externí odkaz:
http://arxiv.org/abs/1609.06849
Autor:
Zinsl, Jonathan, Matthes, Daniel
We propose a fully discrete variational scheme for nonlinear evolution equations with gradient flow structure on the space of finite Radon measures on an interval with respect to a generalized version of the Wasserstein distance with nonlinear mobili
Externí odkaz:
http://arxiv.org/abs/1609.06907
Autor:
Zinsl, Jonathan
We prove the existence of nonnegative weak solutions to a class of second and fourth order nonautonomous nonlinear evolution equations with an explicitly time-dependent mobility function posed on the whole space $\mathbb{R}^d$, for arbitrary $d\ge 1$
Externí odkaz:
http://arxiv.org/abs/1604.07694
Autor:
Zinsl, Jonathan
This article is concerned with the existence of nonnegative weak solutions to a particular fourth-order partial differential equation: it is a formal gradient flow with respect to a generalized Wasserstein transportation distance with nonlinear mobil
Externí odkaz:
http://arxiv.org/abs/1603.01375
Autor:
Plazotta, Simon, Zinsl, Jonathan
Publikováno v:
Journal of Differential Equations 261 (2016), pp. 6806-6855
We study the high-frequency limit of non-autonomous gradient flows in metric spaces of energy functionals comprising an explicitly time-dependent perturbation term which might oscillate in a rapid way, but fulfills a certain Lipschitz condition. On g
Externí odkaz:
http://arxiv.org/abs/1601.04445
We prove the global-in-time existence of nonnegative weak solutions to a class of fourth order partial differential equations on a convex bounded domain in arbitrary spatial dimensions. Our proof relies on the formal gradient flow structure of the eq
Externí odkaz:
http://arxiv.org/abs/1507.05507
Autor:
Zinsl, Jonathan
Publikováno v:
Discrete and Continuous Dynamical Systems 36(5):2915--2930, 2016
We investigate a Poisson-Nernst-Planck type system in three spatial dimensions where the strength of the electric drift depends on a possibly small parameter and the particles are assumed to diffuse quadratically. On grounds of the global existence r
Externí odkaz:
http://arxiv.org/abs/1503.04029
Autor:
Zinsl, Jonathan
Publikováno v:
Comptes Rendus Mathematique 353(9), 849--854 (2015)
We prove the existence of global-in-time weak solutions to a version of the parabolic-parabolic Keller-Segel system in one spatial dimension. If the coupling of the system is suitably weak, we prove convergence of those solutions to the unique equili
Externí odkaz:
http://arxiv.org/abs/1502.01825
Autor:
Zinsl, Jonathan
We consider a system of $n$ nonlocal interaction evolution equations on $\mathbb{R}^d$ with a differentiable matrix-valued interaction potential $W$. Under suitable conditions on convexity, symmetry and growth of $W$, we prove $\lambda$-geodesic conv
Externí odkaz:
http://arxiv.org/abs/1412.3266
Autor:
Zinsl, Jonathan, Matthes, Daniel
Publikováno v:
Calc. Var. PDE 54(4), 3397-3438, 2015
We introduce Wasserstein-like dynamical transport distances between vector-valued densities on the real line. The mobility function from the scalar theory is replaced by a mobility matrix, that is subject to positivity and concavity conditions. Our p
Externí odkaz:
http://arxiv.org/abs/1409.6520