Electron. J. Differential Equations,
Vol. 2019 (2019), No. 83, pp. 1-22.
Difficulties in obtaining finite time blowup for fourth-order semilinear
Schrodinger equations in the variational method frame
Runzhang Xu, Qiang Lin, Shaohua Chen, Guojun Wen, Wei Lian
Abstract:
This article concerns the Cauchy problem for fourth-order semilinear
Schrodinger equations. By constructing a variational problem and some
invariant manifolds, we prove the existence of a global solution.
Then we analyze the difficulties in proving the finite time blowup of the solution
for the corresponding problem in the frame of the variational method.
Understanding the finite time blowup of solutions,
without radial initial data, still remains an open problem.
Submitted January 11, 2019. Published June 24, 2019.
Math Subject Classifications: 35B44, 35G25, 35A01, 35Q55.
Key Words: Fourth-order Schrodinger equation; global solution; blowup;
variational problem; invariant manifolds.
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Runzhang Xu
College of Automation and
College of Mathematical Sciences
Harbin Engineering University
Harbin 150001, China
email: xurunzh@163.com
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Qiang Lin
College of Automation
Harbin Engineering University
Harbin 150001, China
email: Linqiang_edu@126.com
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Shaohua Chen
Department of Mathematics
Cape Breton University
Sydney, NS, B1P 6L2, Canada
email: george_chen@cbu.ca
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Guojun Wen
College of Mathematical Sciences
Harbin Engineering University
Harbin 150001, China
email: 964219363@qq.com
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Wei Lian
College of Automation
Harbin Engineering University
Harbin 150001, China
email: lianwei_1993@163.com
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