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

被引：0

作者：

Pedas, Arvet ^{[1
]}

Vikerpuur, Mikk ^{[1
]}

机构：

[1] Univ Tartu, Inst Math & Stat, Narva St 18, EE-51009 Tartu, Estonia

来源：

APPLIED NUMERICAL MATHEMATICS | 2024年 / 204卷

关键词：

Volterra integral equation; Nonlinear integral equation; Weakly singular integral equation; Boundary singularity; Smoothness of the solution; PIECEWISE POLYNOMIAL COLLOCATION; KERNELS;

D O I：

10.1016/j.apnum.2024.06.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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].

引用

页码：176 / 187

页数：12

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