Symmetry Properties of Positive Solutions of Parabolic Equations on ℝ N : I. Asymptotic Symmetry for the Cauchy Problem
Peter Poláčik · Communications in Partial Differential Equations · 2005
We consider quasilinear parabolic equations on ℝ N satisfying certain symmetry conditions. We prove that bounded positive solutions decaying to zero at spatial infinity are asymptotically radially symmetric about a center. The asymptotic center of symmetry is not fixed a priori (and depends on the solution) but it is independent of time. We also prove a similar theorem on reflectional symmetry.