scholarly journals On the parabolic partial differential equation in two independent variables

1935 ◽  
Vol 064 (6) ◽  
pp. 165-166
Author(s):  
Alfred Rosenblatt
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Independent Variables ◽  
Two Independent Variables

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 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 Time- or Space-Dependent Coefficient Recovery in Parabolic Partial Differential Equation for Sensor Array in the Biological Computing

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Guanglu Zhou ◽  
Boying Wu ◽  
Wen Ji ◽  
Seungmin Rho
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Sensor Array ◽  
Variational Iteration Method ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Variational Iteration

This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to handle. By the variational iteration method, we obtain the exact solution and the unknown coefficients. The results of numerical experiments and stable experiments imply that the variational iteration method is very suitable to solve these inverse problems.

Sign in / Sign up

Export Citation Format

Share Document