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

共 50 条

[31] Boundary stabilization and disturbance rejection for an unstable time fractional diffusion-wave equation
Zhou, Hua-Cheng
Wu, Ze-Hao
Guo, Bao-Zhu
Chen, Yangquan
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2022, 28
[32] An efficient meshless method based on RBFs for the time fractional diffusion-wave equation
Aslefallah M.
Shivanian E.
Afrika Matematika, 2018, 29 (7-8) : 1203 - 1214
[33] Time distributed-order diffusion-wave equation. II. Applications of Laplace and Fourier transformations
Atanackovic, Teodor M.
Pilipovic, Stevan
Zorica, Dusan
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2009, 465 (2106): : 1893 - 1917
[34] Diffusion-Wave Type Solutions to the Second-Order Evolutionary Equation with Power Nonlinearities
Kazakov, Alexander
Lempert, Anna
MATHEMATICS, 2022, 10 (02)
[35] Analysis of the Time Fractional 2-D Diffusion-Wave Equation via Moving Least Square (MLS) Approximation
Shivanian E.
International Journal of Applied and Computational Mathematics, 2017, 3 (3) : 2447 - 2466
[36] Axisymmetric solutions to fractional diffusion-wave equation in a cylinder under Robin boundary condition
Y. Povstenko
The European Physical Journal Special Topics, 2013, 222 : 1767 - 1777
[37] Green Function of the First Boundary-Value Problem for the Fractional Diffusion-Wave Equation in a Multidimensional Rectangular Domain
Pskhu A.V.
Journal of Mathematical Sciences, 2022, 260 (3) : 325 - 334
[38] Approximate symmetry group classification for a nonlinear fractional filtration equation of diffusion-wave type
Lukashchuk, Stanislav Yu.
Saburova, Regina D.
NONLINEAR DYNAMICS, 2018, 93 (02) : 295 - 305
[39] A NOVEL FINITE DIFFERENCE SCHEME FOR TIME FRACTIONAL DIFFUSION-WAVE EQUATION WITH SINGULAR KERNEL
Bouguetof, K.
Haouam, K.
TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2021, 11 (03): : 681 - 688
[40] Sumudu transform method for solving fractional differential equations and fractional Diffusion-Wave equation
Darzi, Rahmat
Mohammadzade, Bahar
Mousavi, Sahar
Beheshti, Rozita
JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2013, 6 (01): : 79 - 84

← 1 2 3 4 5 →