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Global Existence and Uniform Estimates of Solutions to Volume Surface Reaction-Diffusion Systems

Vandana Sharma, IIT Jodhpur
Speaker
Vandana Sharma, IIT Jodhpur
When Jan 29, 2020
from 04:00 PM to 05:00 PM
Where LH 006
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Abstract: We consider coupled reaction-diffusion models where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport, dynamic or Wentzell boundary conditions. We derive Sobolev estimates for linear dynamic initial boundary value problems and combine these with classical potential theory and classical estimates for linear initial boundary value problems to prove local well-posedness. Conservation of mass and other reasonable assumptions afford a priori estimate, and allow us to employ duality arguments to bootstrap sufficiently to obtain global existence, and uniform sup-norm bounds. Systems of this form arise in a number of physical scenarios.

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