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Singularly Perturbed Systems of Volterra Equations
Journal of Applied Analysis, 2002This 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, 2002Several 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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Suboptimization of Singularly Perturbed Control Systems
SIAM Journal on Control and Optimization, 1992The singularly perturbed control system \(\dot z=f_ 1(z,y,u)\), \(z(0)=z_ 0\), \(\varepsilon\dot y=f_ 2(z,y,u)\), \(y(0)=y_ 0\), is studied and compared with the `reduced system' \(\dot z=f_ 1(z,\psi(z,u),u)\), \(z(0)=z_ 0\), where \(y=\psi(z,u)\) is the root of the static equation \(0=f_ 2(z,y,u)\). It is shown that the reduced system approximates the
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Interior Estimates for Singularly Perturbed Problems
Zeitschrift für Analysis und ihre Anwendungen, 1984The solution of the Dirichlet problem for a singularly perturbed elliptic differential equation \epsilon L_1u + L_0u = h of order 2m converges, for
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Singularly Perturbed Discontinuous Systems
1992One of the major obstacles in the use of efficient tools for designing control systems is the high order of equations that describe their behaviour. In many cases they may be reduced to a lower order model by neglecting small time constants or rejecting fast components of the system overall motion.
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Some singular singularly-perturbed problems. II.
1999Summary: This paper continuous part I published in the previous number of the same volume. For the corresponding summary see [ibid. 15, No. 3, 260--271 (1999; Zbl 0968.34015)].
Chang, K. W., Meng, J.
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