oaioai:CiteSeerX.psu:10.1.1.56.5558

Space-Time Behavior in Problems of Hydrodynamic Type: A Case Study

Abstract

We review results concerning normal forms, fronts, pattern formation, and convergence for certain 1-dimensional partial differential equations. The relationship between these results is put into perspective and is supplemented by a series of unpublished results on the convergence problem for parabolic PDE's. The paper does not require special prerequisites and we hope to interest the non-specialist for this nice subject. CONTENTS 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2. The GL-equation as a normal form of the SH-equation . . . . . . . . . . . . 4 3. Uniform bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4. Time-independent solutions . . . . . . . . . . . . . . . . . . . . . . . 8 5. Linear stability analysis . . . . . . . . . . . . . . . . . . . . . . . . 9 6. Fronts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 7. Space-time behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 15 7.1. The case q + = q \G..

Similar works

Full text

thumbnail-image
oaioai:CiteSeerX.psu:10.1.1.56.5558Last time updated on 10/22/2014

This paper was published in CiteSeerX.

Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.