Hyperbolic Property of a Linear Volterra Integro-Differential Operator in Problems of Oscillations of a Viscoelastic Rod

IF 1.5 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-07-29 DOI:10.1134/S106192082502013X

N.A. Rautian, D.V. Georgievskii

引用次数: 0

Abstract

For Volterra integro-differential operators in partial derivatives of the second order, the concept of hyperbolicity with respect to a cone is introduced. It is established that the hyperbolicity with respect to a cone is equivalent to the localization of the support of the fundamental solution of the Volterra integro-differential operator in the conjugate cone. The hyperbolicity with respect to a cone of the integro-differential operator of oscillations of a viscoelastic rod with a fractional-exponential relaxation function is proved.

DOI 10.1134/S106192082502013X

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粘弹性杆振动问题中线性Volterra积分-微分算子的双曲性质

对于二阶偏导数的Volterra积分微分算子，引入了关于锥的双曲性的概念。建立了锥的双曲性等价于共轭锥上Volterra积分微分算子的基本解的支撑点的局域化。证明了具有分数指数松弛函数的粘弹性杆的振动积分微分算子对锥的双曲性。DOI 10.1134 / S106192082502013X

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.