The nonlinear case

1986 ◽  
pp. 55-67
Author(s):  
Jacob Kogan
Keyword(s):  
Nonlinear Case

scholarly journals On some nonlinear inverse problems in elasticity

2011 ◽  
Vol 38 (2) ◽  
pp. 125-154 ◽  
Author(s):  
S. Andrieux ◽  
H.D. Bui
Keyword(s):  
Inverse Problems ◽  
Closed Form ◽  
Variational Equation ◽  
Material Constant ◽  
Displacement Discontinuity ◽  
Crack Plane ◽  
Nonlinear Case ◽  
Elastic Solids ◽  
Linear Inverse Problems ◽  
Statics And Dynamics

In this paper, we make a review of some inverse problems in elasticity, in statics and dynamics, in acoustics, thermoelasticity and viscoelasticity. Crack inverse problems have been solved in closed form, by considering a nonlinear variational equation provided by the reciprocity gap functional. This equation involves the unknown geometry of the crack and the boundary data. It results from the symmetry lost between current fields and adjoint fields which is related to their support. The nonlinear equation is solved step by step by considering linear inverse problems. The normal to the crack plane, then the crack plane and finally the geometry of the crack, defined by the support of the crack displacement discontinuity, are determined explicitly. We also consider the problem of a volumetric defect viewed as the perturbation of a material constant in elastic solids which satisfies the nonlinear Calderon?s equation. The nonlinear problem reduces to two successive ones: a source inverse problem and a Volterra integral equation of the first kind. The first problem provides information on the inclusion geometry. The second one provides the magnitude of the perturbation. The geometry of the defect in the nonlinear case is obtained in closed form and compared to the linearized Calderon?s solution. Both geometries, in linearized and nonlinear cases, are found to be the same.

scholarly journals About Two-dimensional Mathematical Model of Contaminant Migration in Unsaturated Catalytic Porous Media with Traps

2020 ◽  
pp. 25-28
Author(s):  
Anatolyy Vlasyuk ◽  
Viktor Zhukovskyy ◽  
Nataliia Zhukovska ◽  
Serhiy Kraychuk
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Moisture Transfer ◽  
Physical Problem ◽  
Two Dimensional ◽  
Contaminant Migration ◽  
Nonlinear Case ◽  
The Finite Difference Method ◽  
Saline Solutions ◽  
Assessment Strategies

This paper proposes an approach for the computer simulation of complex physical problem of contaminant migration through unsaturated catalytic porous media to the filter-trap. The corresponding mathematical model in the two-dimensional nonlinear case is presented. The model includes detailed considerations of the moisture transfer of saline solutions under the generalized Darcy’s and Cluta’s laws in different subregions of soil. The numerical solution of the boundary value problem was found by the finite difference method and proposed the algorithm for computer implementation. The proposed algorithm may be used for creating software with effective risk assessment strategies and predicting the cleaning and further useful use of the soil massifs.

Adaptive H ∞ Control Using Coprime Factors and Set-Membership Identification: The Nonlinear Case

1995 ◽  
Vol 28 (14) ◽  
pp. 227-232
Author(s):  
G. Ferreres ◽  
V. Fromion ◽  
M. M’Saad
Keyword(s):  
Nonlinear Case ◽  
Set Membership

scholarly journals Steady nonlinear diffusion-driven flow

2009 ◽  
Vol 629 ◽  
pp. 299-309 ◽  
Author(s):  
M. A. PAGE ◽  
E. R. JOHNSON
Keyword(s):  
Temperature Gradient ◽  
Mass Flux ◽  
Previous Analysis ◽  
Leading Order ◽  
Nonlinear Case ◽  
Flow Temperature ◽  
Outer Flow ◽  
Background Temperature ◽  
Sloping Surface ◽  
Associated Mass

An imposed normal temperature gradient on a sloping surface in a viscous stratified fluid can generate a slow steady flow along a thin ‘buoyancy layer’ against that surface, and in a contained fluid the associated mass flux leads to a broader-scale ‘outer flow’. Previous analysis for small values of the Wunsch–Phillips parameter R is extended to the nonlinear case in a contained fluid, when the imposed temperature gradient is comparable with the background temperature gradient. As for the linear case, a compatibility condition relates the buoyancy-layer mass flux along each sloping boundary to the outer-flow temperature gradient. This condition allows the leading-order flow to be determined throughout the container for a variety of configurations.

Numerical analysis for relativistic stars with nonlinear equation of state in AdS

2015 ◽  
Vol 30 (21) ◽  
pp. 1550105
Author(s):  
Zhonghua Li ◽  
Limei Zhang
Keyword(s):  
Equation Of State ◽  
Energy Density ◽  
Total Mass ◽  
Critical Dimension ◽  
De Sitter ◽  
Nonlinear Case ◽  
Maximal Mass ◽  
Ads Spacetime ◽  
Central Energy ◽  
Two Parameters

It is known that for self-gravitating radiation stars in anti-de Sitter (AdS) spacetime, there is a critical dimension, larger than it, the stars always maintain stability with any central energy density [Formula: see text]; smaller than it, there is a maximal mass for the [Formula: see text] and when the [Formula: see text] continues to increase, the total mass of stars becomes a function of the [Formula: see text], and the function appears as an oscillation behavior and therefore the stars become unstable. In this paper we extend this study to the nonlinear case, in this case the equation of state is [Formula: see text], in AdS spacetime, where a and b are two constant parameters. For the nonlinear case,the equations of gravitational field are more complicated, so the relation of total mass to the central energy density is numerically investigated. In particular, the effect of the two parameters a and b and the relation between spacetime dimension d, mass and [Formula: see text] are analyzed. We find that the critical dimension changes when the parameters a and b vary, namely the equation of state. In particular, the critical dimension decreases when b decreases.

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