SPACE-TIME BEHAVIOR IN PROBLEMS OF HYDRODYNAMIC TYPE - A CASE-STUDY

We review results concerning normal forms, fronts, pattern formation, and convergence for certain one-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 The relationship between these results is put into perspective and is supplemented by a series of unpublished results on the convergence problem for parabolic PDEs. The paper does not require special prerequisites and we hope to interest the non-specialist in this nice subject.