Characteristics for First-Order Wave Equations
Wave splitting for first order systems of equations
... Systems of first-order partial differential equations are considered and the possible de- composition of the solutions in forward and backward propagating is investigated. After a review of a customary ...
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FIRST-ORDER DIFFERENTIAL EQUATIONS
... ferential equations simultaneously for every over some time interval (finite or ...these equations in isolation to find solutions or since each derivative depends on both x and ...parametric ...
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Separable First Order Differential Equations
... For example, suppose we want the value of c corresponding to the initial condition y(0) = 2.[r] ...
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System of First Order Differential Equations
... of First Order Differential Equations In this chapter, we will discuss system of first order differential equa- ...of equations that involving the unknown functions and their ...
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Existence of ground states for fourth order wave equations
... linear equations y iv + c 2 y ′′ + y = 0, where y ≥ − 1, and y iv + c 2 y ′′ = 1, where y ≤ ...both equations were constructed which matched at the boundary y = −1 and which tended to zero exponentially as ...
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First-Order Singular and Discontinuous Differential Equations
... Another modification of the concepts of lower and upper solutions concerns the possibility of allowing jumps in their graphs. Since the task of finding a pair of lower and upper solutions is by no means easy in general, ...
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First and second order dynamic equations with impulse
... 1. Introduction We first briefly survey the recent results for existence of solutions to first-order problems with fixed-time impulses. Periodic boundary conditions using upper and lower solutions ...
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Oscillation of First Order Neutral Difference Equations
... Abstract In this paper, we consider a class of first order neutral difference equations of the form ∆ [ r ( n )( x ( n ) + p ( n ) x ( n − τ ))] + q ( n ) x ( n − σ ) = 0, n ≥ n 0 . (∗) Some ...
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Systems of First Order Linear Differential Equations
... A matrix is a rectangular array of objects (called entries). Those entries are usually numbers, but they can also include functions, vectors, or even other matrices. Each entry’s position is addressed by the row and ...
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8 Hyperbolic Systems of First-Order Equations
... Motivation. Recall that all linear, constant-coefficient second-order hyperbolic equations can be written as u tt − ∆u + . . . = 0 through a change of variables, where “. . . ” represents ...
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A simple implementation of PML for second-order elastic wave equations
... a first-order ordinary differential equa- tion (ODE), where the stresses are needed, but the stresses are only intermediate variables from the constitutive ...simulate wave propagation in isotropic, ...
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Qualitative Research of First Order Linear Difference Equations
... Otherwise, the solution is said to be nonoscillatory. An equation is oscillatory if all its solutions are oscillatory. In the past few years, there has been an increasing interest in the study of oscillatory behavior of ...
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On Exact Controllability of First Order Impulsive Differential Equations
... References 1 S. Gao, L. Chen, J. J. Nieto, and A. Torres, “Analysis of a delayed epidemic model with pulse vaccination and saturation incidence,” Vaccine, vol. 24, no. 35-36, pp. 6037–6045, 2006. 2 J. J. Nieto, “Basic ...
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Nonoscillation of First Order Dynamic Equations with Several Delays
... of first-order delay-difference and differential equations has been extensively studied in the last two ...differential equations have their analogues for delay difference ...difference ...
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On the existence of solutions for a class of first order differential equations
... In order to obtain a more useful form of Lemma 2.2, we state the following lemma. Lemma 2.3 (see [3]). Let X be a Banach space and C ⊂ X be compact, then the closed convex hull of C is compact. Lemma 2.4. Let X be ...
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Numerical Solution of First Order Ordinary Differential Equations
... Differential equations arise from many problems in oscillations of mechanical and electrical systems, bending of beams, conduction of heat, velocity of chemical reactions ...
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Numerical Solution of First Order Ordinary Differential Equations
... Differential equations arise from many problems in oscillations of mechanical and electrical systems, bending of beams, conduction of heat, velocity of chemical reactions ...
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In this Chapter we first consider first order PDE and then move to 1- dimensional wave equation which we analyze by the method of characteristics.
... Problem 9. Often solution in the form of travelling wave u = (x vt) is sought for more general equations. Here we are interested in the bounded solutions, especially in those with (x) either tending to 0 as ...
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15.1. Exact Differential Equations. Exact First-Order Equations. Exact Differential Equations Integrating Factors
... Differential Equations • Integrating Factors Exact Differential Equations In Section ...differential equations to growth and decay ...differential equations and using them in real-life ...the ...
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A New Approach In Determining Solution Of The Differential Equations And The First Order Partial Differential Equations
... non-homogeneous) first order differ- ential equations and formation of differential equations in short meth- ods and solving the second order linear differential equations with ...
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