Quasilinear parabolic equations with a Lévy Laplacian for functions of infinite number of variables - Kovtun, I. I.; Feller, M. N. (Methods of Functional Analysis and Topology, 2008)
We construct solutions to initial, boundary and initial-boundary value problems for quasilinear parabolic equations with an infinite dimensional Lévy Laplacian Δ _L, U(t,x)t=Δ_LU(t,x)+f_0(U(t,x)), in fundamental domains of a Hilbert space. The solution is defined in the functional class where a solution of the corresponding problem for the heat equation U(t,x)t=Δ_LU(t,x) exists.