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arXiv · 1711.02966

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

Marco Bonacini·Barbara Niethammer·Juan Velázquez
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Abstract

We consider Smoluchowski's coagulation equation in the case of the diagonal kernel with homogeneity $γ>1$. 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 behaviour of solutions to the self-similar equation as the parameter $b$ changes.

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Marco Bonacini, Barbara Niethammer, Juan Velázquez. 2018-12-13. Self-similar gelling solutions for the coagulation equation with diagonal kernel. https://doi.org/10.1016/j.anihpc.2018.09.001

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