Results 151 to 160 of about 10,372 (181)

Singularly Perturbed Volterra Integral Equations

SIAM Journal on Applied Mathematics, 1987
The authors study the singularly perturbed Volterra integral equation \[ \epsilon u(t)=\int^{t}_{0}K(t-s)F(u(s),s) ds,\quad t\geq 0, \] where \(\epsilon\) is a small parameter, with the objective of developing a methodology that yields the appropriate ''inner'' and ''outer'' integral equations, each of which is defined on the whole domain of interest ...
Angell, J. S., Olmstead, W. E.
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Singularly perturbed pseudoparabolic equation

Mathematical Methods in the Applied Sciences, 2016
An asymptotic expansion of the contrasting structure‐like solution of the generalized Kolmogorov–Petrovskii–Piskunov equation is presented. A generalized maximum principle for the pseudoparabolic equations is developed. This, together with the generalized differential inequalities method, allows to prove the consistence and convergence of the ...
Bykov, Alexey, Panin, Alexander, Sharlo, Alena   +2 more
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Singularly Perturbed Volterra Integral Equations II

SIAM Journal on Applied Mathematics, 1987
The authors extend the formal methodology for the asymptotic analysis of singularly perturbed Volterra integral equations developed by themselves [ibid. 47, 1-14 (1987; Zbl 0616.45009)] to several problems of the form \[ \epsilon (a(\epsilon)u'(t)+b(\epsilon)u(t))=\int^{t}_{0}k(t,s;\epsilon)f[u(s),s ;\epsilon]\quad ds+f(t;\epsilon),\quad t\geq 0 ...
Angell, J. S., Olmstead, W. E.
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Singularly perturbed difference equations

Journal of Difference Equations and Applications, 1999
Comstock and Hsiao have given a method for constructing asymptotic approximations for singularly perturbed linear difference equations with two point boundary conditions and for verifying the corre...
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Singularly Perturbed Systems of Volterra Equations

Journal of Applied Analysis, 2002
This paper studies the behaviour of the solution \(u(t,\varepsilon)\) of the system of Volterra integral equations \[ \varepsilon u(t) = f(t) + \int_0^t A(t,s)u(s)\,ds, \quad 0 \leq t \leq T, \] as the positive parameter \(\epsilon\) tends to zero. Both \(f\) and \(A\) are continuous, and the eigenvalues of \(A(t,t)\) are supposed to be negative.
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Singularly Perturbed Volterra Integro-differential Equations

Quaestiones Mathematicae, 2002
Several investigations have been made on singularly perturbed integral equations. This paper aims at presenting an algorithm for the construction of asymptotic solutions and then provide a proof asymptotic correctness to singularly perturbed systems of Volterra integro-differential equations.
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Singularly Perturbed Linear Stochastic Ordinary Differential Equations

SIAM Journal on Mathematical Analysis, 1979
Singularly perturbed linear differential equations with random forcing functions have recently been studied as models of control and filtering systems. The analysis in these studies has been somewhat formal, and important properties of the boundary layer behavior have been neglected as a consequence.
Blankenship, G., Sachs, S.
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Singularly Perturbed Differential-Difference Equations

1993
A delay equation $$ v\dot x\left( x \right) = - x\left( t \right) + f\left( {x\left( t \right)} \right),x\left( t \right):{R^ + } \to R, v >0, $$ (3.1) and some its generalizations have recently become a matter of interest in the theory of differential equations.
A. N. Sharkovsky, Yu. L. Maistrenko, E. Yu. Romanenko   +2 more
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Metastable Periodic Patterns in Singularly Perturbed Delayed Equations

Journal of Dynamics and Differential Equations, 2010
The equation \[ \varepsilon\dot{x}(t)=-x(t)+f(x(t-1)) \] is considered in the limit \(\varepsilon\to 0\) for both cases of Positive Feedback (PF) and Negative Feedback (NF) by the nonlinearity \(f\), which is assumed to be odd in the positive feedback case.
Grotta-Ragazzo, C., Malta, C.P., Pakdaman, Khashayar   +2 more
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Nonlinear singularly perturbed problems of ultra parabolic equations

Applied Mathematics and Mechanics, 2008
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Lin, Surong, Mo, Jiaqi
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