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

作者：Craddock Mark^*; Yakubovich Semyon

来源：Journal of Differential Equations, 2017, 263(11): 7412-7447.

DOI：10.1016/j.jde.2017.08.012

• Hyperbolic PDEs
• Integral equations
• Fundamental solutions
• Cauchy problems
• Harmonic analysis

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.

• 出版日期2017-12-5