Self-similar gelling solutions for the coagulation equation with diagonal kernel

  • Marco Bonacini

    University of Bonn, Institute for Applied Mathematics, Endenicher Allee 60, 53115 Bonn, Germany
  • Barbara Niethammer

    University of Bonn, Institute for Applied Mathematics, Endenicher Allee 60, 53115 Bonn, Germany
  • Juan J.L. Velázquez

    University of Bonn, Institute for Applied Mathematics, Endenicher Allee 60, 53115 Bonn, Germany
Self-similar gelling solutions for the coagulation equation with diagonal kernel cover
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Abstract

We consider Smoluchowski's coagulation equation in the case of the diagonal kernel with homogeneity γ>1\gamma > 1. In this case the phenomenon of gelation occurs and solutions lose mass at some finite time. The problem of the existence of self-similar solutions involves a free parameter b, and one expects that a physically relevant solution (i.e. nonnegative and with sufficiently fast decay at infinity) exists for a single value of b, depending on the homogeneity γ. We prove this picture rigorously for large values of γ. In the general case, we discuss in detail the behavior of solutions to the self-similar equation as the parameter b changes.

Cite this article

Marco Bonacini, Barbara Niethammer, Juan J.L. Velázquez, Self-similar gelling solutions for the coagulation equation with diagonal kernel. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 3, pp. 705–744

DOI 10.1016/J.ANIHPC.2018.09.001