New classes of non-convolution integral equations arising from Lie symmetry analysis of hyperbolic PDEs

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Craddock, Mark¹  Yakubovich, Semyon² 

[1] Univ Technol Sydney, Sch Math & Phys Sci, POB 123, Broadway, NSW 2007, Australia

[2] Univ Porto, Fac Sci, Dept Pure Math, Campo Alegre St 687, P-416900 Oporto, Portugal

关键词: Hyperbolic PDEs;    Integral equations;    Fundamental solutions;    Cauchy problems;    Harmonic analysis;   

DOI  :  10.1016/j.jde.2017.08.012

来源: Elsevier

【 摘 要 】

In this paper we consider some new classes of integral equations that arise from Lie symmetry analysis. Specifically, we consider the task of obtaining solutions of a Cauchy problem for some classes of second order hyperbolic partial differential equations. Our analysis leads to new integral equations of non-convolution type, which can be solved by classical methods. We derive solutions of these integral equations, which in turn lead to solutions of the associated Cauchy problems. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free