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Search: MSC category 34E10 ( Perturbations, asymptotics )

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1. CMB Online first

Alhasanat, Ahmad; Ou, Chunhua
Periodic steady-state solutions of a liquid film model via a classical method
In this paper, periodic steady-state of a liquid film flowing over a periodic uneven wall is investigated via a classical method. Specifically, we analyze a long-wave model that is valid at the near-critical Reynolds number. For the periodic wall surface, we construct an iteration scheme in terms of an integral form of the original steady-state problem. The uniform convergence of the scheme is proved so that we can derive the existence and the uniqueness, as well as the asymptotic formula, of the periodic solutions.

Keywords:film flow, classical methods, asymptotic analysis
Categories:34E05, 34E10, 34E15

2. CMB 2017 (vol 60 pp. 364)

Preda, Ciprian
On the Roughness of Quasinilpotency Property of One–parameter Semigroups
Let $\mathbf{S}:=\{S(t)\}_{t\geq0}$ be a C$_0$-semigroup of quasinilpotent operators (i.e. $\sigma(S(t))=\{0\}$ for each $t\gt 0$). In the dynamical systems theory the above quasinilpotency property is equivalent to a very strong concept of stability for the solutions of autonomous systems. This concept is frequently called superstability and weakens the classical finite time extinction property (roughly speaking, disappearing solutions). We show that under some assumptions, the quasinilpotency, or equivalently, the superstability property of a C$_0$-semigroup is preserved under the perturbations of its infinitesimal generator.

Keywords:one-parameter semigroups, quasinilpotency, superstability, essential spectrum
Categories:34D05, 34D10, 34E10

3. CMB 2011 (vol 55 pp. 3)

Agarwal, Ravi P.; Mustafa, Octavian G.
On a Local Theory of Asymptotic Integration for Nonlinear Differential Equations
We improve several recent results in the asymptotic integration theory of nonlinear ordinary differential equations via a variant of the method devised by J. K. Hale and N. Onuchic The results are used for investigating the existence of positive solutions to certain reaction-diffusion equations.

Keywords:asymptotic integration, Emden-Fowler differential equation, reaction-diffusion equation
Categories:34E10, 34C10, 35Q35

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