具有Balakrishnan-Taylor阻尼的Kirchhoff-Carrier型Robin-Dirichlet问题解的渐近展开式

IF 0.8 4区数学 Q2 MATHEMATICS

Filomat Pub Date : 2023-01-01 DOI:10.2298/fil2308321n

Huu-Bao Nhan, B. Nam, L. Ngoc, N. Long

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引用次数: 0

摘要

本文研究了一类具有Balakrishnan-Taylor阻尼的Kirchhoff-Carrier型非线性波动方程的Robin-Dirichlet问题。首先，在初始数据的适当条件下，证明了一个弱解的局部存在唯一性。其次，建立了高阶小参数解的渐近展开式。使用的主要工具是非线性项的线性化方法和Faedo-Galerkin方法，以及高阶多项式展开和多变量函数的泰勒展开的关键引理。

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Asymptotic expansion of solutions for the Robin-Dirichlet problem of Kirchhoff-Carrier type with Balakrishnan-Taylor damping

In this paper, we consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type with Balakrishnan-Taylor damping. First, under suitable conditions on the initial data, the local existence and uniqueness of a weak solution are proved. Next, an asymptotic expansion of solutions in a small parameter with high order is established. The used main tools are the linearization method for nonlinear terms together with the Faedo-Galerkin method, and the key lemmas of the expansion of high-order polynomials and the Taylor expansion for multi-variable functions.

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