Finite-time Blow-up of L-weak Solutions of an Aggregation Equation

نویسندگان

  • ANDREA L. BERTOZZI
  • JEREMY BRANDMAN
چکیده

Abstract. We consider the aggregation equation ut+∇· [(∇K)∗u)u]=0 with nonnegative initial data in L(R)∩L(R) for n≥2. We assume that K is rotationally invariant, nonnegative, decaying at infinity, with at worst a Lipschitz point at the origin. We prove existence, uniqueness, and continuation of solutions. Finite time blow-up (in the L norm) of solutions is proved when the kernel has precisely a Lipschitz point at the origin.

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تاریخ انتشار 2008