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Self-similar gelling solutions for the coagulation equation with diagonal kernel
We consider Smoluchowski's coagulation equation in the case of the diagonal
kernel with homogeneity . 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 , and one
expects that a physically relevant solution (i.e. nonnegative and with
sufficiently fast decay at infinity) exists for a single value of ,
depending on the homogeneity . We prove this picture rigorously for
large values of . In the general case, we discuss in detail the
behaviour of solutions to the self-similar equation as the parameter
changes
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