Propagation properties of the solutions of a nonlinear parabolic equation

Abstract

Some propagation properties, including a discussion on the existence of compactly supported solutions and the asymptotics of the interfaces thereby determined, are considered for the Cauchy problem u t =(|u x | m-1 ·u x ) x in S=ℝ×(0,∞); u(x,0)=u 0 (x)≥0 in ℝ where m>1. An expanded version of these results with a discussion on the case 0<m<1 can be found in Commun. Partial Differ. Equations 7, 1381-1402 (1982).