We consider quasilinear parabolic equations on ℝN 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.
Bibliographical noteFunding Information:
The author is supported in part by NSF grant DMS-0400702.
- Asymptotic symmetry
- Cauchy problem
- Positive bounded solutions
- Quasilinear parabolic equations