Boundary-value problems for the wave equation with Lévy Laplacian in the Gâteaux class

• Date: 2009
• Main Authors: Feller, M. N., Феллер, М. Н.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2009
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3122
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We present the solutions of the initial-value problem in the entire space and the solutions of the boundary-value and initial-boundary-value problems for the wave equation $$\frac{∂^2U(t,x)}{∂x^2} = Δ_LU(t,x)$$ with infinite-dimensional Lévy Laplacian $Δ_L$ in the class of Gâteaux functions.