scholarly journals Mathematical modeling of seismoelectric effect of the second sort generated by flat elastic waves in porous moisture saturated environments

2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Igor Moskowsky ◽  
Oleg Balaban ◽  
Olga Fedorova ◽  
Andrey Kochetkov
Keyword(s):  
Mathematical Modeling ◽  
Elastic Waves ◽  
Porous Moisture

Pure modes for elastic waves in crystals: mathematical modeling and search

2011 ◽  
Vol 220 (1-4) ◽  
pp. 199-207 ◽  
Author(s):  
A. I. Kochaev ◽  
R. A. Brazhe
Keyword(s):  
Mathematical Modeling ◽  
Elastic Waves

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

Cerebral Blood Circulation in Premature Infants by Means of Mathematical Modeling

2015 ◽  
Vol 46 (S 01) ◽  
Author(s):  
R. Lampe ◽  
N. Botkin ◽  
V. Turova ◽  
T. Blumenstein ◽  
A. Alves-Pinto
Keyword(s):  
Mathematical Modeling ◽  
Premature Infants ◽  
Blood Circulation ◽  
Cerebral Blood Circulation
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