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Appearance of anomalous singularities in a semilinear parabolic equation

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  • The Cauchy problem for a parabolic partial differential equation with a power nonlinearity is studied. It is known that in some parameter range, there exists a time-local solution whose singularity has the same asymptotics as that of a singular steady state. In this paper, a sufficient condition for initial data is given for the existence of a solution with a moving singularity that becomes anomalous in finite time.
    Mathematics Subject Classification: Primary: 35K55; Secondary: 35B33.


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