Convergence of solution to nonlinear dispersive equations
- 1 January 1982
- journal article
- Published by Taylor & Francis in Communications in Partial Differential Equations
- Vol. 7 (8) , 959-1000
- https://doi.org/10.1080/03605308208820242
Abstract
Summary:DiPerna and Majda generalized Young measures so that it is possible to describe "in the limit" oscillation as well as concentration effects of bounded sequences in $L^p$-spaces. Here the complete description of all such measures is stated, showing that the "energy" put at "infinity" by concentration effects can be described in the limit basically by an arbitrary positive Radon measure. Moreover, it is shown that concentration effects are intimately related to rays (in a suitable locally convex geometry) in the set of all DiPerna-Majda measures. Finally, a complete characterization of extreme points and extreme rays is establishedKeywords
This publication has 1 reference indexed in Scilit:
- The zero dispersion limit for the Korteweg-deVries KdV equationProceedings of the National Academy of Sciences, 1979