Global well-posedness and scattering of a generalized nonlinear fourth-order wave equation

2017 ◽  
Author(s):  
Chuanwei Gao ◽  
Jing Lu
Keyword(s):  
Wave Equation ◽  
Fourth Order ◽  
Well Posedness ◽  
Fourth Order Wave Equation

Fourth order wave equation with nonlinear strain and logarithmic nonlinearity

2019 ◽  
Vol 141 ◽  
pp. 185-205 ◽  
Author(s):  
Runzhang Xu ◽  
Wei Lian ◽  
Xiangkun Kong ◽  
Yanbing Yang
Keyword(s):  
Wave Equation ◽  
Fourth Order ◽  
Nonlinear Strain ◽  
Fourth Order Wave Equation

scholarly journals Global existence and blowup in infinite time for a fourth order wave equation with damping and logarithmic strain terms

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yue Pang ◽  
Xingchang Wang ◽  
Furong Wu
Keyword(s):  
Wave Equation ◽  
Fourth Order ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Energy ◽  
Contraction Mapping Principle ◽  
Logarithmic Strain ◽  
Infinite Time ◽  
Positive Initial Energy ◽  
Fourth Order Wave Equation

<p style='text-indent:20px;'>We consider the well-posedness of solution of the initial boundary value problem to the fourth order wave equation with the strong and weak damping terms, and the logarithmic strain term, which was introduced to describe many complex physical processes. The local solution is obtained with the help of the Galerkin method and the contraction mapping principle. The global solution and the blowup solution in infinite time under sub-critical initial energy are also established, and then these results are extended in parallel to the critical initial energy. Finally, the infinite time blowup of solution is proved at the arbitrary positive initial energy.</p>

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