scholarly journals Nonlinear integral inequality in two independent variables

1988 ◽  
Vol 11 (1) ◽  
pp. 115-119
Author(s):  
P. T. Vaz ◽  
S. G. Deo
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Integral Inequality ◽  
Nonlinear Partial Differential Equation ◽  
Partial Differential ◽  
Independent Variables ◽  
Nonlinear Integral Inequality ◽  
Nonlinear Inequality ◽  
Two Independent Variables

In this note, the authors obtain a generalization of the integral inequality of Bihari [1] to a nonlinear inequality in two independent variables. With the aid of this inequality a bound for the solution of a nonlinear partial differential equation is established.

scholarly journals Memoir on the integration of partial differential equations of the second order in three independent variables, when an intermediary integral does not exist in general

1898 ◽  
Vol 62 (379-387) ◽  
pp. 283-285
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
General Feature ◽  
Partial Differential ◽  
First Order ◽  
Independent Variables ◽  
Dependent Variables ◽  
Two Independent Variables

The general feature of most of the methods of integration of any partial differential equation is the construction of an appropriate subsidiary system and the establishment of the proper relations between integrals of this system and the solution of the original equation. Methods, which in this sense may be called complete, are possessed for partial differential equations of the first order in one dependent variable and any number of independent variables; for certain classes of equations of the first order in two independent variables and a number of dependent variables; and for equations of the second (and higher) orders in one dependent and two independent variables.

scholarly journals Different forms of Euler’s theorem forhomogeneous functions to solve partial differential equation

2021 ◽  
Vol 12 (2) ◽  
pp. 2810-2813
Author(s):  
Amit Kumar, Et. al.
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
Independent Variables ◽  
Euler’S Theorem ◽  
Different Order ◽  
Two Independent Variables

In this paper we will discuss Euler’s theorem for homogenous functions to solve different order partial differential equations. We will see that how we can predict the solution of partial differential Equation using different approaches of this theorem. In fact we also consider the case when more than two independent variables will be involved in the partial differential equation whenever dependent functions will be homogenous functions. We will throw a light on one method called Ajayous rules to predict the solution of homogenous partial differential equation.

scholarly journals On an integral inequality inN-independent variables

1984 ◽  
Vol 7 (3) ◽  
pp. 455-467 ◽  
Author(s):  
Olusola Akinyele
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Integral Inequality ◽  
Pointwise Estimates ◽  
Hyperbolic Partial Differential Equation ◽  
Partial Differential ◽  
Independent Variables ◽  
Estimates Of Solutions ◽  
Non Linear ◽  
Linear Integral

We present a new non-linear integral inequality of the Gronwall-Bellman-Bihari type inn-independent variables with application to pointwise estimates of solutions of a certain class of non-linear hyperbolic partial differential equation.

scholarly journals EVOLUTION OF MODULATIONAL INSTABILITY IN TRAVELLING WAVE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION

2020 ◽  
Vol 5 (1) ◽  
pp. 1-7
Author(s):  
Ram Dayal Pankaj ◽  
Arun Kumar ◽  
Chandrawati Sindhi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Solution ◽  
Modulational Instability ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Partial Differential ◽  
Jacobian Elliptic Functions

The Ritz variational method has been applied to the nonlinear partial differential equation to construct a model for travelling wave solution. The spatially periodic trial function was chosen in the form of combination of Jacobian Elliptic functions, with the dependence of its parameters

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