LOCAL AND NORM BEHAVIOR OF BLOWUP SOLUTIONS TO A PARABOLIC SYSTEM OF CHEMOTAXIS

  • Senba, Takasi (Department of Applied Mathematics, Faculty of Technology, Miyazaki University) ;
  • Suzuki, Takashi (Department of Mathematics, Graduate School of Science, Osaka University)
  • Published : 2000.11.01

Abstract

We study a parabolic system of chemotaxis introduced by E.F. Keler and L.A. Segel. First, norm behaviors of the blow-up solution are proven. Then some kind of symmetry breaking and the concentration toward the boundary follow when the L$^1$norm of the initial value is less than 8$\pi$. Meanwhile a method of rearrangement is porposed toprove an inequality of Trudinger-Moser's type.

Keywords

References

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