Study of a nonlinear renewal equation with diffusion
Speaker 
Dr. Bhargav Kumar, University of Hyderabad


When 
Jan 09, 2017
from 04:00 PM to 05:00 PM 
Where  LH 006 
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Abstract: We consider a nonlinear age structured McKendrickvon Foerster population model with diffusion term (MVD). We prove the existence and uniqueness of solution (both weak and classical) of the MVD equation. For the weak solution, we also prove the convergence of the solution to its steady state as time tends to infinity using the generalized relative entropy inequality and Poincare Writinger type inequality. In the case of the classical solution, we also establish that, the solution of MVD equation converges pointwise to the solution of its steady state equations as time tends to infinity using the method of subsolution and supersolution.
We propose a numerical scheme for the linear MVD equation. We discretize the time variable to get a system of second order ordinary differential equations. Convergence of the scheme is established using the stability estimates by introducing Rothe’s function.