Volterra Integral Equations: An Introduction to Theory and Applications
Volterra Integral Equations: An Introduction to Theory and Applications
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DOI：
10.1017/9781316162491
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发表时间：
2017-01
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影响因子：
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通讯作者：
H. Brunner
中科院分区：
文献类型：
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作者：
H. Brunner
本书全面介绍了线性和非线性沃尔泰拉积分方程（VIEs）的理论，从沃尔泰拉的基本贡献和由此产生的经典理论到最近的发展，包括具有各种延迟的沃尔泰拉泛函积分方程，具有高度振荡核的vie，以及具有非紧算子的vie。它将作为一个“踏脚石”，对先进的vie理论的文献，使读者在理论的艺术的当前状态。每一章都包含大量的练习，从说明或补充理论的常规问题扩展到具有挑战性的开放研究问题。在记忆效应起关键作用的现象的数学建模中，视点理论日益重要的作用用大约30个具体的例子来说明，每章末尾的注释都有补充的参考资料，作为进一步阅读的指导。
This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels, and VIEs with non-compact operators. It will act as a'stepping stone'to the literature on the advanced theory of VIEs, bringing the reader to the current state of the art in the theory. Each chapter contains a large number of exercises, extending from routine problems illustrating or complementing the theory to challenging open research problems. The increasingly important role of VIEs in the mathematical modelling of phenomena where memory effects play a key role is illustrated with some 30 concrete examples, and the notes at the end of each chapter feature complementary references as a guide to further reading.