The C$^1$ stability of slow manifolds for a system of singularly perturbed evolution equations

Daniel Ševčovič

Displaying similar documents to “The C$^1$ stability of slow manifolds for a system of singularly perturbed evolution equations”

Smoothness of unordered curves in two-dimensional strongly competitive systems

Janusz Mierczyński (1999)

Applicationes Mathematicae

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It is known that in two-dimensional systems of ODEs of the form $^{i} = x^{i} f^{i} (x)$ with $\partial f^{i} / \partial x^{j} < 0$ (strongly competitive systems), boundaries of the basins of repulsion of equilibria consist of invariant Lipschitz curves, unordered with respect to the coordinatewise (partial) order. We prove that such curves are in fact of class $C^{1}$ .

Limiting behavior of global attractors for singularly perturbed beam equations with strong damping

Daniel Ševčovič (1991)

Commentationes Mathematicae Universitatis Carolinae

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The limiting behavior of global attractors $𝒜_{ε}$ for singularly perturbed beam equations $ε^{2} \frac{\partial^{2} u}{\partial t^{2}} + ε δ \frac{\partial u}{\partial t} + A \frac{\partial u}{\partial t} + α A u + {g (∥ u ∥}_{1 / 4}^{2}) A^{1 / 2} u = 0$ is investigated. It is shown that for any neighborhood $𝒰$ of $𝒜_{0}$ the set $𝒜_{ε}$ is included in $𝒰$ for $ε$ small.

Discretization and some qualitative properties of ordinary differential equations about equilibria.

Garay, B.M. (1993)

Acta Mathematica Universitatis Comenianae. New Series

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On $C^{j}$ -closeness of invariant foliations under numerics.

Farkas, G. (2000)

Acta Mathematica Universitatis Comenianae. New Series

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Differential operators with generalized constant coefficients.

Pilipović, S., Scarpalézos, D. (1996)

Portugaliae Mathematica

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Multidimensional singular $λ$ -lemma.

Rayskin, Victoria (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Regularity of solutions of parabolic equations with coefficients depending on t and parameters

T. Winiarska (1992)

Annales Polonici Mathematici

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The main object of this paper is to study the regularity with respect to the parameter h of solutions of the problem $d u / d t + A_{h} (t) u (t) = f_{h} (t)$ , $u (0) = u_{h}^{0}$ . The continuity of u with respect to both h and t has been considered in [6].

Displaying similar documents to “The C$^1$ stability of slow manifolds for a system of singularly perturbed evolution equations”

Smoothness of unordered curves in two-dimensional strongly competitive systems

Limiting behavior of global attractors for singularly perturbed beam equations with strong damping

Discretization and some qualitative properties of ordinary differential equations about equilibria.

On C j -closeness of invariant foliations under numerics.

Differential operators with generalized constant coefficients.

Multidimensional singular λ -lemma.

Regularity of solutions of parabolic equations with coefficients depending on t and parameters

On $C^{j}$ -closeness of invariant foliations under numerics.

Multidimensional singular $λ$ -lemma.