JournalsprimsVol. 39 , No. 4DOI 10.2977/prims/1145476046

Spiral Traveling Wave Solutions of Nonlinear Diffusion Equations Related to a Model of Spiral Crystal Growth

  • Toshiko Ogiwara

    Josai University, Saitama, Japan
  • Ken-Ichi Nakamura

    University of Electro-Communications, Tokyo, Japan
Spiral Traveling Wave Solutions of Nonlinear Diffusion Equations Related to a Model of Spiral Crystal Growth cover

Abstract

This paper is concerned with nonlinear diffusion equations related to a model of the motion of screw dislocations on crystal surfaces. We prove the existence, uniqueness and asymptotic stability of a rotating and growing solution with a timeindependent profile, which we call a spiral traveling wave solution.