Fourth order wave equations with nonlinear strain and source terms

By Yacheng Liu, Runzhang Xu. 2007

55 citations recorded by the source corpus.

Abstract In this paper we study the initial boundary value problem for fourth order wave equations with nonlinear strain and source terms. First we introduce a family of potential wells and prove the invariance of some sets and vacuum isolating of solutions. Then we obtain a threshold result of global existence and nonexistence. Finally we discuss the global existence of solutions for the problem with critical initial condition I ( u 0 ) ⩾ 0 , E ( 0 ) = d . So the Esquivel-Avila's results are generalized and improved.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c08389831b046dc3efdd2b542caba1b8e21e0baa

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In Applied Mathematics

1. Runzhang Xu
2. Wei-Cheng Lian
3. Vicentiu D. Rădulescu
4. Dušan D. Repovš
5. Zhijun Zhang
6. Anouar Bahrouni
7. Marius Ghergu
8. V. Ruadulescu

In Control and Systems Engineering

1. Wei-Cheng Lian
2. Vicentiu D. Rădulescu
3. Nan Zhao
4. Yanbing Yang
5. Runzhang Xu
6. Marius Ghergu
7. Ahmed Mohammed

In Mathematical Physics

1. Wei-Cheng Lian
2. Vicentiu D. Rădulescu
3. Nan Zhao
4. Yanbing Yang
5. Runzhang Xu
6. Zuodong Yang

Citations in the corpus

• Global well-posedness for a class of fourth-order nonlinear strongly damped wave equations (2019, background): “Terms included in the equation utt ∆2u ∆u ∑i=1 ∂ ∂xi σi(uxi ) ∆ut |ut |r−1ut f(u) Results • • • Global existence for E(0) < d (see [5]) • • • • Describe the elastoplastic microstructure models for longitudinal motion of an elastoplastic bar [4] • • • • Global existence and asymptotic behavior for E(”