A strongly degenerate diffusion equation with strong absorption | Zendy

Winkler Michael | Zendy

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A strongly degenerate diffusion equation with strong absorption

Author(s) -

Winkler Michael

Publication year - 2004

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200310221

Subject(s) - mathematics , degenerate energy levels , bounded function , initial value problem , diffusion equation , weak solution , absorption (acoustics) , mathematical analysis , cauchy problem , extinction (optical mineralogy) , diffusion , mathematical physics , pure mathematics , chemistry , physics , thermodynamics , quantum mechanics , mineralogy , economy , acoustics , economics , service (business)

It is shown that the Cauchy problem in ℝ for the strongly degenerate parabolic equation$$ u_t = u^p u_{xx} - u^{-q} \chi _{ \{u>o \} }\, , \quad p \ge 1 \, , \quad q > -1 \, , $$has a nonnegative weak solution for any nonnegative bounded continuous initial datum, provided that q ≤ p – 1, while there is no (continuous) weak solution for q > p – 1. The evolution of the spatial positivity set { u ( t ) > 0}, continuity of the free boundary and the extinction rate are also investigated. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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