Unique determination of cyclic instability state in flow liquefaction of sand

2020 ◽  
pp. 1-9
Author(s):  
Xueqian Ni ◽  
Bin Ye ◽  
Guanlin Ye ◽  
Feng Zhang
Keyword(s):  
Unique Determination ◽  
Flow Liquefaction

Rigid versus unique determination of protein structures with geometric buildup

2007 ◽  
Vol 2 (3) ◽  
pp. 319-331 ◽  
Author(s):  
Di Wu ◽  
Zhijun Wu ◽  
Yaxiang Yuan
Keyword(s):  
Protein Structures ◽  
Unique Determination

scholarly journals Recovery of Time-Dependent Coefficient on Riemannian Manifold for Hyperbolic Equations

2017 ◽  
Vol 2019 (16) ◽  
pp. 5087-5126 ◽  
Author(s):  
Yavar Kian ◽  
Lauri Oksanen
Keyword(s):  
Riemannian Manifold ◽  
Hyperbolic Equations ◽  
Lorentzian Manifold ◽  
Cauchy Data ◽  
Time Dependent ◽  
Unique Determination ◽  
Data Set ◽  
Dependent Potential ◽  
Calderón Problem

Abstract Given $(M,g)$, a compact connected Riemannian manifold of dimension $d \geq 2$, with boundary $\partial M$, we study the inverse boundary value problem of determining a time-dependent potential $q$, appearing in the wave equation $\partial_t^2u-\Delta_g u+q(t,x)u=0$ in ${\overline M}=(0,T)\times M$ with $T>0$. Under suitable geometric assumptions we prove global unique determination of $q\in L^\infty({\overline M})$ given the Cauchy data set on the whole boundary $\partial {\overline M}$, or on certain subsets of $\partial {\overline M}$. Our problem can be seen as an analogue of the Calderón problem on the Lorentzian manifold $({\overline M}, dt^2 - g)$.

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