Regularizing Effects of Homogeneous Evolution Equations
Abstract
It is well-known that solving the initial-value problem for the heat equation forward in time takes a 'rough' initial temperature into a temperature which is smooth at later times t > greater than 0. One aspect of this is the validity of certain estimates on tut when u is a solution of the heat equation. In this paper we prove related estimates on nonlinear evolution equations which are governed by homogeneous nonlinearities. The results apply to classes of nonlinear diffusion equations and to conservation laws. The results are interesting from the point of view of identifying a new 'regularization' mechanism and the estimates themselves cast new light on the nature of the solutions of some initial-value problems with rough initial data.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1980
- Accession Number
- ADA086561
Entities
People
- Michael G. Crandall
- Philippe Benilan
Organizations
- University of Wisconsin–Madison