22 papers
Comparison inequalities for Dirichlet-to-Neumann maps
Denis S. Grebenkov, Michael Levitin, Karl-Mikael Perfekt +1
We prove comparison inequalities for Dirichlet-to-Neumann maps corresponding to different non-positive Helmholtz parameters. For convex domains our bounds are sharp, and the result…
Reaction-Diffusion Processes with Surface Autocatalysis
Denis S. Grebenkov
Autocatalytic processes underlie diverse systems in which replication is triggered at interfaces, including heterogeneous catalysis on solid substrates, enzyme activity at membrane…
A unifying approach to diffusive transport in annealed heterogeneous media
Yann Lanoiselée, Denis S. Grebenkov, Gianni Pagnini
We introduce the concept of Randomly Modulated Gaussian Processes as a unifying framework for elaborating, analyzing and classifying anomalous diffusion models in annealed heteroge…
Surviving the Attack of the Clones
Denis S. Grebenkov
We consider a population dynamics model in which each diffusing particle that hits a catalytic surface can split into two independent copies (clones). The particles of such a growi…
The exterior Steklov problem for Euclidean domains
Lukas Bundrock, Alexandre Girouard, Denis S. Grebenkov +2
We investigate the Steklov eigenvalue problem in an exterior Euclidean domain. First, we present several formulations of this problem and establish the equivalences between them. N…
Diffusion-driven autocatalytic dynamics on a sphere
Denis S. Grebenkov
We study the collective dynamics of independent particles that diffuse outside a spherical surface, on which they are replicated with a prescribed catalytic rate. In spatial dimens…