Quasi-Linear Equations of First-Order

2009 ◽  
pp. 225-263
Author(s):  
Emmanuele DiBenedetto
Keyword(s):  
Linear Equations ◽  
First Order

Partially Invariant Solutions for Two-dimensional Ideal MHD Equations

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1219-1229 ◽  
Author(s):  
D.-A. Becker ◽  
E. W. Richter
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Mhd Equations ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
First Order ◽  
Partially Invariant Solutions ◽  
Quasilinear Systems ◽  
Ideal Mhd ◽  
Non Linear Equations

AbstractA generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.

First Order Linear Equations

2001 ◽  
pp. 51-79
Author(s):  
Martin Bohner ◽  
Allan Peterson
Keyword(s):  
Linear Equations ◽  
Order Linear ◽  
First Order

scholarly journals Minimization of Deviations of Gear Real Tooth Surfaces Determined by Coordinate Measurements

1993 ◽  
Vol 115 (4) ◽  
pp. 995-1001 ◽  
Author(s):  
F. L. Litvin ◽  
C. Kuan ◽  
J. C. Wang ◽  
R. F. Handschuh ◽  
J. Masseth ◽  
...  
Keyword(s):  
Linear Equations ◽  
Least Square Method ◽  
Least Square ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Overdetermined System ◽  
Entire Surface ◽  
First Order ◽  
Tooth Surfaces ◽  
Coordinate Measurements

The deviations of a gear’s real tooth surface from the theoretical surface are determined by coordinate measurements at the grid of the surface. A method has been developed to transform the deviations from Cartesian coordinates to those along the normal at the measurement locations. Equations are derived that relate the first order deviations with the adjustment to the manufacturing machine tool settings. The deviations of the entire surface are minimized. The minimization is achieved by application of the least-square method for an overdetermined system of linear equations. The proposed method is illustrated with a numerical example for hypoid gear and pinion.

An Asymptotic Solution for the Response of Face-Sheet Delaminations/Debonds Under Compression

2000 ◽  
Author(s):  
George A. Kardomateas ◽  
Haiying Huang
Keyword(s):  
Transverse Shear ◽  
Critical Strain ◽  
Linear Equations ◽  
Face Sheet ◽  
Beam Equation ◽  
System Of Linear Equations ◽  
Postbuckling Behavior ◽  
Nonlinear Beam ◽  
First Order ◽  
Higher Order Terms

Abstract The buckling and initial postbuckling behavior of face-sheet delaminations or face-sheet/core debonds is studied by a perturbation procedure. The procedure is based on the nonlinear beam equation with transverse shear included, and an asymptotic expansion of the load and deformation quantities. First the characteristic equation for the critical load is formulated and this is a nonlinear algebraic equation. Subsequently, the first order load is found from a system of linear equations and the initial postbuckling behavior can thus be studied. The procedure can be easily expanded to the higher order terms. The effect of transverse shear is illustrated with results on the critical strain and the initial postbuckling displacement.

ABOUT UNIQUENESS OF WEAK SOLUTIONS TO FIRST ORDER QUASI-LINEAR EQUATIONS

2002 ◽  
Vol 12 (11) ◽  
pp. 1599-1615 ◽  
Author(s):  
J. NIETO ◽  
J. SOLER ◽  
F. POUPAUD
Keyword(s):  
Conservation Laws ◽  
Weak Solutions ◽  
Entropy Solution ◽  
Linear Equations ◽  
Particle Method ◽  
Entropy Condition ◽  
First Order

In this paper we give a criterion to discriminate the entropy solution to quasi-linear equations of first order among weak solutions. This uniqueness statement is a generalization of Oleinik's criterion, which makes reference to the measure of the increasing character of weak solutions. The link between Oleinik's criterion and the entropy condition due to Kruzhkov is also clarified. An application of this analysis to the convergence of the particle method for conservation laws is also given by using the Filippov characteristics.

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