Results 301 to 310 of about 817,111 (369)

On a first order partial differential equation with the nonlocal boundary condition

, 2014
In this paper, the initial value problem for the first order partial differential equation with the nonlocal boundary condition is studied. In applications, the stability estimates for the first order partial differential equation with the nonlocal ...
A. Ashyralyev, Sueda Nur Tekalan, A. S. Erdogan   +2 more
semanticscholar   +1 more source

Solvability of a first order linear partial differential equation

Communications on Pure and Applied Mathematics, 1963
F. Treves, Louis Nirenberg
openaire   +3 more sources

FORMULATION OF DIRAC EQUATION FOR AN ARBITRARY FIELD FROM A SYSTEM OF LINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS

, 2018
In our previous works we formulated Dirac equation for a free quantum particle and Maxwell field equations for the electromagnetic field from a system of linear first order partial differential equations.
Vu Ho
semanticscholar   +1 more source

First-order Partial Differential Equations [PDF]

, 2009
In this chapter we will discuss the first order linear partial differential equations, homogeneous and inhomogeneous. Partial differential equations of first order are used to model traffic flow on a crowded road, blood flow through an elastic-walled tube, shock waves and as special cases of the general theories of gas dynamics and hydraulics.
openaire   +1 more source

LOCAL CLASSIFICATION OF NON-LINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS

, 1975
ContentsIntroduction Chapter I. Geometry of non-linear first order differential equations § 1. Jets § 2. Non-linear differential equations and many-valued solutions § 3. Contact diffeomorphisms and symmetries § 4. The algebra of contact vector fields § 5.
V. Lychagin
semanticscholar   +1 more source

Partial Differential Equations of the First Order

2020
We consider linear partial differential equations of the first order. A partial differential equation is linear if the dependent variables, i.e., the functions that are being solved for, appear only to the first power and the coefficients, i.e., the factors the derivatives are multiplied by, do not contain the dependent variables.
openaire   +2 more sources

Double Walsh series solution of first-order partial differential equations

, 1978
A double Walsh series is introduced to represent approximately functions of two independent variables, and is then applied to analyse single as well as simultaneous first-order partial differential equations.
Y. Shih, Joung-Yi Han
semanticscholar   +1 more source

First-Order Partial Differential Equations

1983
Partial differential equations have been studied much less than ordinary differential equations. Part of the theory—that of a single partial differential equation of the first order—can be reduced to the study of special ordinary differential equations, the so-called characteristic equations.
openaire   +2 more sources

Minimax solutions of first-order partial differential equations

, 1996
Contents Introduction ?1. Some notions and results from non-smooth analysis ?2. Main definitions ?3. Equivalence of minimax and viscosity solutions ?4. Generalized characteristics ?5. Piecewise smooth solutions ?6.
A. I. Subbotin
semanticscholar   +1 more source

Multivalued solutions of first-order partial differential equations

, 1998
The concept of multivalued solution of a first-order partial differential equation is introduced. This is a development of the concept of a minimax solution, the definition of which is based on the weak invariance property with respect to the ...
A. Lakhtin, A. I. Subbotin
semanticscholar   +1 more source