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Two Initial Value Problems Approach for Solving Singular Perturbations Problems
Singular Perturbation Initial Value Problems Asymptotic Power Series Expansions
2013/1/30
In this paper, we presented an initial value approach for solving singularly perturbed two point boundary value problems with the boundary layer at one end (left or right). By employing asymptotic pow...
Normally Elliptic Singular Perturbations and Persistence of Homoclinic Orbits
Normally Elliptic Singular Perturbations Persistence of Homoclinic Orbits
2011/1/14
We consider a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. We first derive and j...
Global-in-time Uniform Convergence for Linear Hyperbolic-Parabolic Singular Perturbations
Parabolic equations Damped hyperbolic equations Singular perturbations
2007/12/12
We consider the Cauchy problem ${\varepsilon}{u_{\ep}}''+\delta{u_{\ep}}'+A{u_{\varepsilon}}=0,$ ${u_{\varepsilon}}(0)=u_0, $ ${u_{\varepsilon}}'(0)=u_{1},$ where ${\varepsilon}>0$, $\delta>0$, $H$ is...