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  1. No Access

    Article

    Animal Shapes, Modal Analysis, and Visualization of Motion (IV): Geometric Constructions and Implementation

    We address computer implementation and technology issues in geometric constructions for mathematical and computational modeling purposes, especially regarding 3D finite-element mesh generation for large scale ...

    **g Yang, Goong Chen, Chunqiu Wei, Alexey Sergeev… in The Journal of Geometric Analysis (2023)

  2. No Access

    Article

    Animal Shapes, Modal Analysis, and Visualization of Motion (I): Horse and Camel

    Eigenfunctions and eigenvalues of physical systems and engineering structures can reveal many of the system’s fundamental features and, therefore, become a basis for the study of inverse problems. In this seri...

    Goong Chen, **gtong Huang, Chunqiu Wei, **g Yang… in The Journal of Geometric Analysis (2023)

  3. No Access

    Article

    Animal Shapes, Modal Analysis, and Visualization of Motion (III): Giraffe, Duck, Goose, T-Rex Dinosaur, and the Flying Modes of Eagle

    This paper contains more varieties of animals, including the giraffe, bird species duck, goose and eagle, and the T-Rex dinosaur. They range across mammals, birds and reptiles. For each of them, we present the...

    **g Yang, Goong Chen, Chunqiu Wei, Alexey Sergeev… in The Journal of Geometric Analysis (2023)

  4. No Access

    Article

    Animal Shapes, Modal Analysis, and Visualization of Motion (II): Dynamics and Fourier Decomposition

    This paper begins with solving the linear elastodynamic equation with forcing by expanding it into Fourier series. We then proceed to prove the conservation laws of momentum, angular momentum, and energy. We i...

    Goong Chen, Chunqiu Wei, Alexey Sergeev, **g Yang… in The Journal of Geometric Analysis (2023)

  5. No Access

    Article

    Lower Bounds of Optimal Exponentials of Thickness in Geometry Rigidity Inequality for Shells

    The optimal exponentials of thickness in the geometry rigidity inequality of shells represent the geometry rigidity of the shells. The author obtains that the lower bounds of the optimal exponentials are 4/3, ...

    Pengfei Yao in Journal of Systems Science and Complexity (2021)

  6. No Access

    Article

    Boundary controllability of structural acoustic systems with variable coefficients and curved walls

    This paper studies a structural acoustic model consisting of an interior acoustic wave equation with variable coefficients and a coupled Kirchhoff plate equation with a curved middle surface. By the Riemannian...

    Fengyan Yang, Pengfei Yao, Goong Chen in Mathematics of Control, Signals, and Systems (2018)

  7. No Access

    Article

    Weighted L2-estimates of solutions for damped wave equations with variable coefficients

    The authors establish weighted L2-estimates of solutions for the damped wave equations with variable coefficients u tt − divA(x)∇u+au t = 0 in

    Pengfei Yao, Zhifei Zhang in Journal of Systems Science and Complexity (2017)

  8. No Access

    Article

    Decay rates of the hyperbolic equation in an exterior domain with half-linear and nonlinear boundary dissipations

    This paper considers the energy decay of the wave equation with variable coefficients in an exterior domain. The dam** is put on partly the boundary and partly on the interior of the domain. The energy decay...

    Yuxiang Liu, **g Li, Pengfei Yao in Journal of Systems Science and Complexity (2016)

  9. No Access

    Article

    General decay rate estimates for viscoelastic wave equation with variable coefficients

    The authors study decay properties of solutions for a viscoelastic wave equation with variable coefficients and a nonlinear boundary dam** by the differential geometric approach.

    **aomin Cao, Pengfei Yao in Journal of Systems Science and Complexity (2014)

  10. Article

    Editorial

    Goong Chen, Pengfei Yao, Jiongmin Yong… in Journal of Systems Science and Complexity (2010)

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  11. No Access

    Article

    Energy decay for the Cauchy problem of the linear wave equation of variable coefficients with dissipation

    Decay of the energy for the Cauchy problem of the wave equation of variable coefficients with a dissipation is considered. It is shown that whether a dissipation can be localized near infinity depends on the c...

    Pengfei Yao in Chinese Annals of Mathematics, Series B (2010)

  12. No Access

    Article

    Global smooth solutions for semilinear Schrödinger equations with boundary feedback on 2-dimensional Riemannian manifolds

    This paper considers the existence of global smooth solutions of semilinear schrödinger equation with a boundary feedback on 2-dimensional Riemannian manifolds when initial data are small. The authors show tha...

    Li Deng, Pengfei Yao in Journal of Systems Science and Complexity (2009)

  13. No Access

    Article

    Observability inequalities for thin shells

    We consider the exact controllability problem from boundary for thin shells. Under some checkable geometric assumptions on the middle surface, we establish the observability inequalities via the Bochner techni...

    Shugen Chai, Pengfei Yao in Science in China Series A: Mathematics (2003)