University of Toronto
                  PDE/Applied Math/Analysis Seminar
                    Wednesday 4 April, 3:10-4:00pm
                          Fields Insitute



SPEAKER:  Wilfred Gangbo

TITLE:    Variational methods for the $1$--d Euler-Poisson system

ABSTRACT: We consider the set $M$ of Borel probability measures on 
	  $R,$ of bounded second moment,  endowed with the Wasserstein 
	  metric $W_2.$ We study a specific Lagrangians $L$ defined on 
	  its tangent bundle. If $H$ is the Hamiltonian associated to 
	  $L$, given an initial value function $U_0$ defined on $M$ and 
	  which is $\lambda$-convex, there is a viscosity solution to 
	  the infinite dimensional Hamilton-Jacobi equation 
	    $\partial_t U + H(\mu, \nabla_\mu U)=0,$  
	  for small times $t$, with the prescribed initial value 
	  function $U_0$. We prove that its characteristics are unique 
	  solution of the one-dimensional Euler-Poisson system with 
	  prescribed endpoints. These paths conserve the Hamiltonian 
	  even when the measures has a singular part. 

	  This is a joint work with T. Nguyen and A, Tudorascu. 




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University of Toronto PDE/Applied Math/Analysis Seminar 
http://www.math.toronto.edu/appmath/

2006-2007 organizers:
          Pieter Blue           pblue@ math.toronto.edu
          Almut Burchard        almut@ math.toronto.edu
          Robert McCann		mccann@ math.toronto.edu
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