论一类非线性 Volterra 积分方程奇点解的正则性

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-06-12 DOI:10.1016/j.apnum.2024.06.008

Arvet Pedas, Mikk Vikerpuur

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引用次数: 0

摘要

我们研究有界区间 [0,b] 上非线性 Volterra 第二类积分方程解的平滑性。基础方程积分算子的核可能具有对角奇异性和边界奇异性。有关它们的信息可通过某些估计值给出。为了描述此类方程解的正则性，我们证明解属于 (0,b] 上光滑函数的适当加权空间，解的导数在区间 [0,b] 的左端点可能存在奇点。

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On the regularity of solutions to a class of nonlinear Volterra integral equations with singularities

We study the smoothness properties of solutions to nonlinear Volterra integral equations of the second kind on a bounded interval $[0, b]$ . The kernel of the integral operator of the underlying equation may have a diagonal singularity and a boundary singularity. Information about them is given through certain estimates. To characterize the regularity of solutions of such equations we show that the solution belongs to an appropriately weighted space of smooth functions on $(0, b]$ , with possible singularities of the derivatives of the solution at the left endpoint of the interval $[0, b]$ .

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.