Grow up and slow decay in the critical Sobolev case | Zendy

Марек Фила | Zendy; John R. King | Zendy

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Grow up and slow decay in the critical Sobolev case

Author(s) -

Марек Фила,

John R. King

Publication year - 2012

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2012.7.661

Subject(s) - sobolev space , dimension (graph theory) , space (punctuation) , zero (linguistics) , nonlinear system , physics , mathematical analysis , mathematics , mathematical physics , pure mathematics , quantum mechanics , computer science , operating system , linguistics , philosophy

We present conjectures on asymptotic behaviour of threshold solutions of the Cauchy problem for a semilinear heat equation with Sobolev critical nonlinearity. The conjectures say that, depending on the decay rate of initial data and the space dimension, the threshold solutions may grow up, stabilize, or decay to zero as $t→∞$. The rates of grow up or decay are computed formally using matched asymptotics.

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