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4 papers · 2 filters
Existence of solutions of the hyperbolic Keller-Segel model
Benoit Perthame, Anne-Laure Dalibard
We are concerned with the hyperbolic Keller-Segel model with quorum sensing, a model describing the collective cell movement due to chemical signalling with a flux limitation for h…
Doubling Properties of Caloric Functions
L. Escauriaza, F. J. FernÁndez, S. Vessella
We prove local quantitative estimates of unique continuation for solutions to parabolic equations: doubling properties and two-sphere one-cylinder inequalities.
Rough solutions for the periodic Korteweg-de Vries equation
M. Gubinelli
We show how to apply ideas from the theory of rough paths to the analysis of low-regularity solutions to non-linear dispersive equations. Our basic example will be the one dimensio…
Relativistic hydrogenic atoms in strong magnetic fields
Jean Dolbeault, Maria J. Esteban, Michael Loss
In the Dirac operator framework we characterize and estimate the ground state energy of relativistic hydrogenic atoms in a constant magnetic field and describe the asymptotic regim…