An exact minimax penalty function approach to solve multitime variational problems

2020 ◽  
Vol 54 (3) ◽  
pp. 637-652 ◽  
Author(s):  
Anurag Jayswal ◽  
Preeti
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Variational Problem ◽  
Penalty Function ◽  
Function Method ◽  
Variational Problems ◽  
Penalty Function Method ◽  
Optimal Solutions ◽  
Partial Differential ◽  
Penalty Function Approach

This paper aims to examine an appropriateness of the exact minimax penalty function method applied to solve the partial differential inequation (PDI) and partial differential equation (PDE) constrained multitime variational problems. The criteria for equivalence between the optimal solutions of a multitime variational problem with PDI and PDE constraints and its associated unconstrained penalized multitime variational problem is studied in this work. We also present some examples to validate the results derived in the paper.

scholarly journals New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp-Function Method

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hasibun Naher ◽  
Farah Aini Abdullah ◽  
M. Ali Akbar
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solutions ◽  
Traveling Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equation ◽  
Traveling Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions ◽  
Higher Dimensional

We construct new analytical solutions of the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher-dimensional nonlinear partial differential equation.

The Establishment of Mathematics Model of Velocity Field in Strip Cast-Rolling Deforment Area

2008 ◽  
Vol 575-578 ◽  
pp. 566-571
Author(s):  
Bin Yu Sun ◽  
Shi Jian Yuan
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Velocity Field ◽  
Function Method ◽  
Research Problem ◽  
Mathematics Model ◽  
Flow Function ◽  
Partial Differential ◽  
Average Unit ◽  
Strip Cast

According to the N-S equation in fluid mechanics, it is analyzed the rheological properties of strip cast-rolling deforment area with flow function method. The research problem can be simplified into 2-D when the wide of cast-rolling strip are greater than thickness. But, it still difficult to find solution for established two-dimensional partial differential equation directly. A mathematics model of velocity field in the cast-rolling area has been built by flow function method. The model not only satisfies the continues equation, the condition of no-compression and velocity boundary, but it also make the most possible to solute partial differential equation. So, in the future continue research, it has created possible conditions for saluting the mathematics model of average unit compression stress distribution in the cast-rolling deforment area.

scholarly journals Studying on Kudryashov-Sinelshchikov dynamical equation arising in mixtures liquid and gas bubbles

2021 ◽  
pp. 247-247
Author(s):  
Haci Baskonus ◽  
Adnan Mahmud ◽  
Kalsum Abdulrahman Muhamad ◽  
Tanfer Tanriverdi ◽  
Wei Gao
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Function Method ◽  
Dynamical Equation ◽  
Nonlinear Partial Differential Equation ◽  
Gas Bubbles ◽  
Partial Differential ◽  
Wave Solutions

In this paper, some new exact traveling and oscillatory wave solutions to the Kudryashov-Sinelshchikov nonlinear partial differential equation are investigated by using Bernoulli sub-equation function method. Profiles of obtained solutions are plotted.

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