D'Alembert Formula for Diffusion-Wave Equation

被引：2

作者：

Pskhu, A. V. ^{[1
]}

机构：

[1] Russian Acad Sci, Inst Appl Math & Automat, Kabardino Balkarian Sci Ctr, Nalchik 360000, Kabardino Balka, Russia

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2023年 / 44卷 / 02期

关键词：

diffusion-wave equation; Liouville fractional derivative; d'Alembert formula; BOUNDARY-VALUE PROBLEM; FRACTIONAL DIFFUSION; CAUCHY-PROBLEM;

D O I：

10.1134/S1995080223020312

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a representation of solutions for diffusion-wave equations as a sum of two solutions of the first order PDEs. Fractional differentiation is given by the Liouville fractional derivative. The representation is an analogue of the d'Alembert formula known for the wave equation. In the case of an infinite rectangular domain (half-strip), we give relations that connect the traces of the solutions involved in the representation on the boundary of the domain.

引用

页码：644 / 652

页数：9

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