scholarly journals Determination of singular time-dependent coefficients for wave equations from full and partial data

2018 ◽  
Vol 12 (3) ◽  
pp. 745-772 ◽  
Author(s):  
Guanghui Hu ◽  
◽  
Yavar Kian ◽  
Keyword(s):  
Wave Equations ◽  
Time Dependent ◽  
Partial Data ◽  
Singular Time

Determination of time-dependent sources and parameters of nonlocal diffusion and wave equations from final data

2020 ◽  
Vol 23 (6) ◽  
pp. 1678-1701
Author(s):  
Jaan Janno
Keyword(s):  
Wave Equations ◽  
Fractional Laplacian ◽  
Source Term ◽  
Time Derivative ◽  
Sufficient Conditions ◽  
Time Dependent ◽  
Nonlocal Diffusion ◽  
Uniqueness Of Solutions ◽  
Fractional Time Derivative

Abstract Two inverse problems with final overdetermination for diffusion and wave equations containing the Caputo fractional time derivative and a fractional Laplacian of distributed order are considered. They are: 1) the problem to reconstruct a time-dependent source term; 2) the problem to recover simultaneously the source term, the order of the time derivative and the fractional Laplacian. Uniqueness of solutions of these problems is proved. Sufficient conditions for the uniqueness are stricter for the 2nd problem than for the 1st problem.

scholarly journals Determination of time-dependent strengths of salt pillars based on strain energy principle

2019 ◽  
Vol 29 (2) ◽  
pp. 273-279 ◽  
Author(s):  
Prapasiri Junthong ◽  
Supattra Khamrat ◽  
Suratwadee Sartkaew ◽  
Kittitep Fuenkajorn
Keyword(s):  
Strain Energy ◽  
Time Dependent ◽  
Energy Principle

scholarly journals Global existence and decay estimates for nonlinear wave equations with space-time dependent dissipative term

2015 ◽  
Vol 12 (02) ◽  
pp. 249-276
Author(s):  
Tomonari Watanabe
Keyword(s):  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Space Time ◽  
Time Dependent ◽  
Nonlinear Wave Equations ◽  
Energy Estimates ◽  
Space Region ◽  
Decay Estimates ◽  
Dissipative Term

We study the global existence and the derivation of decay estimates for nonlinear wave equations with a space-time dependent dissipative term posed in an exterior domain. The linear dissipative effect may vanish in a compact space region and, moreover, the nonlinear terms need not be in a divergence form. In order to establish higher-order energy estimates, we introduce an argument based on a suitable rescaling. The proposed method is useful to control certain derivatives of the dissipation coefficient.

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