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Global well-posedness for a class of fourth-order nonlinear strongly damped wave equations

  • Wei Lian , Vicenţiu D. Rădulescu ORCID logo , Runzhang Xu ORCID logo EMAIL logo , Yanbing Yang and Nan Zhao
Published/Copyright: September 11, 2019

Abstract

In this paper, we consider the initial boundary value problem for a class of fourth-order wave equations with strong damping term, nonlinear weak damping term, strain term and nonlinear source term in polynomial form. First, the local solution is obtained by using fix point theory. Then, by constructing the potential well structure frame, we get the global existence, asymptotic behavior and blowup of solutions for the subcritical initial energy and critical initial energy respectively. Ultimately, we prove the blowup in finite time of solutions for the arbitrarily positive initial energy case.

MSC 2010: 35L05

Communicated by Giuseppe Mingione


Award Identifier / Grant number: 11871017

Award Identifier / Grant number: 11801114

Award Identifier / Grant number: 2013M540270

Award Identifier / Grant number: LBH-Z15036

Award Identifier / Grant number: 201706685064

Funding statement: This work was supported by the National Natural Science Foundation of China (11871017, 11801114), the China Postdoctoral Science Foundation (2013M540270), the Heilongjiang Postdoctoral Foundation (LBH-Z15036), the Fundamental Research Funds for the Central Universities, and the China Scholarship Council (201706685064). Prof. Vicenţiu D. Rădulescu acknowledges the support throughout the Project MTM2017-85449-P of the DGISPI (Spain).

Acknowledgements

Dr. Yanbing Yang also specially appreciates Prof. Yue Liu for his invitation of visit to UTA.

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Received: 2019-05-16
Revised: 2019-06-22
Accepted: 2019-06-27
Published Online: 2019-09-11
Published in Print: 2021-10-01

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