FINITE TIME BLOW-UP AND GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR PSEUDO-PARABOLIC EQUATION WITH EXPONENTIAL NONLINEARITY | Zendy

Qunfei Long | Zendy; Jianqing Chen | Zendy; Ganshan Yang | Zendy

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FINITE TIME BLOW-UP AND GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR PSEUDO-PARABOLIC EQUATION WITH EXPONENTIAL NONLINEARITY

Author(s) -

Qunfei Long,

Jianqing Chen,

Ganshan Yang

Publication year - 2018

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2018.105

Subject(s) - mathematics , mathematical analysis , nonlinear system , exponential growth , exponential function , parabolic partial differential equation , physics , partial differential equation , quantum mechanics

This paper is concerned with the initial boundary value problem of a class of pseudo-parabolic equation ut − 4u − 4ut + u = f(u) with an exponential nonlinearity. The eigenfunction method and the Galerkin method are used to prove the blow-up, the local existence and the global existence of weak solutions. Moreover, we also obtain other properties of weak solutions by the eigenfunction method.

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