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

Qunfei Long; Jianqing Chen; Ganshan Yang

doi:10.11948/2018.105

2018 Volume 8 Issue 1

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Qunfei Long, Jianqing Chen, Ganshan Yang. FINITE TIME BLOW-UP AND GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR PSEUDO-PARABOLIC EQUATION WITH EXPONENTIAL NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2018, 8(1): 105-122. doi: 10.11948/2018.105

Citation:

Qunfei Long, Jianqing Chen, Ganshan Yang. FINITE TIME BLOW-UP AND GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR PSEUDO-PARABOLIC EQUATION WITH EXPONENTIAL NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2018, 8(1): 105-122. doi: 10.11948/2018.105

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

1 Department of Mathematics & FJKLMAA, FuJian Normal University, FuZhou, 350117, China;
2 Department of Mathematics, Yunnan Nationalities University and Yunnan Normal University, 650031, 650092, China

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Abstract

Abstract

This paper is concerned with the initial boundary value problem of a class of pseudo-parabolic equation u_t -4u -4u_t + 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.
- Pseudo-parabolic equation /
- existence /
- finite time blow-up /
- exponential nonlinearity
MSC: 35K70;35B44;35A01

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References

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