Integral Equations and Partial Differential Equations, vol. IV (V. I. Smirnov)

SIAM Review ◽  
1965 ◽  
Vol 7 (4) ◽  
pp. 572-574
Author(s):  
Michael Yanowitch
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Equations ◽  
Partial Differential

XIV.—On General Dynamics:—I. Hamilton's Partial Differential Equations and the Determination of their Complete Integrals

1913 ◽  
Vol 32 ◽  
pp. 164-174
Author(s):  
A. Gray
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Equations ◽  
Equations Of Motion ◽  
Partial Differential ◽  
General Dynamics ◽  
Elementary Manner ◽  
Derivatives Of

The present paper contains the first part of a series of notes on general dynamics which, if it is found worth while, may be continued. In § 1 I have shown how the first Hamiltonian differential equation is led up to in a natural and elementary manner from the canonical equations of motion for the most general case, that in which the time t appears explicitly in the function usually denoted by H. The condition of constancy of energy is therefore not assumed. In § 2 it is proved that the partial derivatives of the complete integral of Hamilton's equation with respect to the constants which enter into the specification of that integral do not vary with the time, so that these derivatives equated to constants are the integral equations of motion of the system.*

Some Partial Differential Equations of Multivariable Vector Functions and the Integral Equations of Multivariable Vector Functions

2010 ◽  
Vol 159 ◽  
pp. 205-209
Author(s):  
Han Zhang Qu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Equations ◽  
Vector Function ◽  
Weak Topology ◽  
Wavelet Transforms ◽  
Linear Equations ◽  
Continuous Wavelet ◽  
Partial Differential ◽  
Continuous Wavelet Transforms

The relations between the partial differential equations of multivariable vector functions and the integral equations of multivariable vector functions which are correspond to them are discussed. The partial differential linear equations of multivariable vector functions can be transformed into the integral linear equations of multivariable vector functions by using the continuous wavelet transforms of multivariable vector function spaces. The result that in the weak topology the partial differential equations of multivariable vector functions are equivalent to the integral equations of multivariable vector functions which are correspond to them is obtained.

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