Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: The existence of a solution to a generalized Kolmogorov-Petrovskii-Piskunov equation is proved and its asymptotic expansion of the internal transition layer type is constructed as discussed by the authors.
Abstract: The existence of a solution to a generalized Kolmogorov-Petrovskii-Piskunov equation is proved and its asymptotic expansion of the internal transition layer type is constructed The convergence of the asymptotics is proved by applying the asymptotic comparison principle developed for a new class of problems
2 citations
27 May 1960
2 citations
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TL;DR: In this paper, one-frequency approximations of asymptotic solutions by using periodic Ateb-functions were constructed for a non-autonomous wave equation with homogeneous boundary conditions.
Abstract: For a nonautonomous wave equation with homogeneous boundary conditions, we construct one-frequency approximations of asymptotic solutions by using periodic Ateb-functions. Resonance and nonresonance cases are considered.
2 citations
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TL;DR: In this article, an algorithm for constructing asymptotic expansions is presented, and properties of the coefficients of the expansion coefficients are investigated for functions of series, and moment bounds for solutions of linear stochastic differential equations.
Abstract: CONTENTS §1 Introduction §2 Algorithm for constructing asymptotic expansions Formulation of the main results §3 Properties of the coefficients of asymptotic series §4 Proof of Theorem 3 §5 Proof of Theorem 4 §6 Auxiliary lemmas 61 Asymptotic series for functions of series 62 Asymptotic properties of solutions of matrix linear differential equations 63 Strong solutions of stochastic differential equations 64 Moment bounds for solutions of linear stochastic differential equations References
2 citations