Random and periodic homogenization for some nonlinear partial differential equations
by Schwab, Russell William, Ph.D., THE UNIVERSITY OF TEXAS AT AUSTIN, 2009, 108 pages; 3369190

Abstract:

In this dissertation we prove the homogenization for two very different classes of nonlinear partial differential equations and nonlinear elliptic integro-differential equations. The first result covers the homogenization of convex and superlinear Hamilton-Jacobi equations with stationary ergodic dependence in time and space simultaneously. This corresponds to equations of the form: u3t+H&parl0;x 3,t3,D u3,w&parr0;=0 in Rn ×0,T u3=u30 on Rn ×0. The second class of equations is nonlinear integro-differential equations with periodic coefficients in space. These equations take the form, F&parl0;u3,x3 &parr0;=0in D u3=gon Dc, where the operator, F, can be expressed as: F&parl0;u,x3&parr0;= inf asupb &cubl0;fab &parl0;x3&parr0; +Rn &parl0;u&parl0;x+y&parr0;+u&parl0;x-y&parr0;-2u&parl0; x&parr0;&parr0;Kab&parl0;x 3,y&parr0;dy&cubr0;.

 
AdvisersPanagiotis E. Souganidis; Luis A. Caffarelli
SchoolTHE UNIVERSITY OF TEXAS AT AUSTIN
SourceDAI/B 70-08, p. , Sep 2009
Source TypeDissertation
SubjectsMathematics
Publication Number3369190
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