非局部非线性奇摄动问题对数型解的Gevrey渐近性

Q3 Mathematics

Abstract and Applied Analysis Pub Date : 2023-04-24 DOI:10.1155/2023/3025513

S. Malek

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引用次数: 1

摘要

我们研究了一类非线性偏微分方程，它们在复参数ε中奇异摄动，在原点处在复时间变量t中奇异。这些方程结合了时间t上的Fuchsian型微分算子和复平面上水平条上的空间导数，以及作用于参数ε的非局部算子，即0左右的形式单态算子。它们的系数和强迫项在时间上是多项式型和对数型函数，在空间上是有界全纯的。一组对数型的解是通过相对于t的拉普拉斯变换、空间中的λ和傅里叶积分来形成的。此外，一个正式的对数型解被建模，它代表了在原点有界扇区上关于御柱的真解的Gevrey型的共同渐近展开式。

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Gevrey Asymptotics for Logarithmic-Type Solutions to Singularly Perturbed Problems with Nonlocal Nonlinearities

We investigate a family of nonlinear partial differential equations which are singularly perturbed in a complex parameter ϵ and singular in a complex time variable t at the origin. These equations combine differential operators of Fuchsian type in time t and space derivatives on horizontal strips in the complex plane with a nonlocal operator acting on the parameter ϵ known as the formal monodromy around 0. Their coefficients and forcing terms comprise polynomial and logarithmic-type functions in time and are bounded holomorphic in space. A set of logarithmic-type solutions are shaped by means of Laplace transforms relatively to t and ϵ and Fourier integrals in space. Furthermore, a formal logarithmic-type solution is modeled which represents the common asymptotic expansion of the Gevrey type of the genuine solutions with respect to ϵ on bounded sectors at the origin.

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来源期刊

Abstract and Applied Analysis 数学-数学

CiteScore

2.30

自引率

0.00%

发文量

审稿时长

3.5 months

期刊介绍： Abstract and Applied Analysis is a mathematical journal devoted exclusively to the publication of high-quality research papers in the fields of abstract and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimization theory, and control theory. Abstract and Applied Analysis supports the publication of original material involving the complete solution of significant problems in the above disciplines. Abstract and Applied Analysis also encourages the publication of timely and thorough survey articles on current trends in the theory and applications of analysis.