ABSTRACT: The simplified momentum equations of the two-phase flow have been adopted as the basic assumptions in this study. For vessels of small diameter, the shear stress becomes important and the ...

Calculus of variations establishes a framework to determine the extrema of functionals—mappings from functions to real numbers—which has been pivotal in elucidating natural principles such as the ...

Nature Research Intelligence Topics Topic summaries Mathematical Sciences Applied Mathematics Calculus of Variations, Mathematical Aspects of Systems Theory and Control Theory Calculus of variations ...

We give a necessary and sufficient condition for the existence of a local solution of the inverse problem of calculus of variations in terms of the identical vanishing of the variation of a functional ...

Abstract: An alternate sufficiency proof for the fixed end-point isoperimetric problem in the calculus of variations is presented. This technique not only shows how the problem need not be transformed ...

Calculus to the level of ODEs, partial derivative and multiple integrals, some knowledge of PDEs helpful but not essential. Students should have a certain comfort level with dealing with advanced ...

ABSTRACT: This paper presents, an efficient approach for solving Euler-Lagrange Equation which arises from calculus of variations. Homotopy analysis method to find an approximate solution of ...