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Singularly Perturbed Differential/Algebraic Equations.
1994Abstract : In this paper, singularly perturbed nonlinear differential/algebraic equations (DAEs) are considered and a proof of the existence and uniqueness of a solution is given. Asymptotic expansions for such a solution are obtained and proved to be uniformly convergent.
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On existence of kink and antikink wave solutions of singularly perturbed Gardner equation
Mathematical Methods in the Applied Sciences, 2020Zhenshu Wen
exaly
Invariant manifolds for singularly perturbed parabolic equations
1994We consider a system in which a differential equation is coupled with a singularly perturbed semilinear evolution equation, namely: \[ \begin{cases} \begin{array}{c} \overset{\dot{x}=f\left(t,x,y,\epsilon\right)}{}\\ \epsilon\dot{y}=A\left(t,x\right)y+g\left(t,x,y,\epsilon\right) \end{array}\end{cases} \] We will prove that, for small $\epsilon$ , the ...
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Singularly perturbed difference equations in optimal control problems
IEEE Transactions on Automatic Control, 1981G Blankenship
exaly