Boundary-value problems for a nonlinear parabolic equation with Lévy Laplacian resolved with respect to the derivative

• Date: 2010
• Main Authors: Kovtun, I. I., Feller, M. N., Ковтун, И. И., Феллер, М. Н.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2010
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2964
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We present the solutions of boundary-value and initial boundary-value problems for a nonlinear parabolic equation with Lévy Laplacian $∆_L$ resolved with respect to the derivative $$\frac{∂U(t,x)}{∂t}=f(U(t,x),Δ_LU(t,x))$$ in fundamental domains of a Hilbert space.