Global existence via a multivalued operator for an Allen-Cahn-Gurtin equation | Zendy

Michel Pierre | Zendy; Morgan Pierre | Zendy

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Global existence via a multivalued operator for an Allen-Cahn-Gurtin equation

Author(s) -

Michel Pierre,

Morgan Pierre

Publication year - 2013

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2013.33.5347

Subject(s) - mathematics , measure (data warehouse) , operator (biology) , lebesgue measure , monotone polygon , absolute continuity , lebesgue integration , monotonic function , type (biology) , allen–cahn equation , mathematical analysis , computer science , geometry , ecology , biochemistry , chemistry , repressor , database , biology , transcription factor , gene

International audienceThe main goal of this paper is to prove existence of global solutions in time for an Allen-Cahn-Gurtin model of pseudo-parabolic type. Local solutions were known to "blow up" in some sense in finite time. It is proved that the equation is actually governed by a monotone-like operator. It turns out to be multivalued and measure-valued. The measures are singular with respect to the Lebesgue measure. This operator allows to extend the local solutions globally in time and to fully solve the evolution problem. The asymptotic behavior is also analyzed

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