Open Access

Quasilinear parabolic equations with a Lévy Laplacian for functions of infinite number of variables

Abstract

We construct solutions to initial, boundary and initial-boundary value problems for quasilinear parabolic equations with an infinite dimensional Lévy Laplacian $\Delta _L$, $$\frac{\partial U(t,x)}{\partial t}=\Delta_LU(t,x)+f_0(U(t,x)),$$ 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 $\frac {\partial U(t,x)}{\partial t}=\Delta_LU(t,x)$ exists.

Article Information

 Title Quasilinear parabolic equations with a Lévy Laplacian for functions of infinite number of variables Source Methods Funct. Anal. Topology, Vol. 14 (2008), no. 2, 117-123 MathSciNet MR2432760 Copyright The Author(s) 2008 (CC BY-SA)

Authors Information

M. N. Feller
Obolonsky prospect 7, ap. 108, Kyiv, 04205, Ukraine

I. I. Kovtun
National Agricultural University, 15 Geroiv Oborony, Kyiv, 03041, Ukraine

Citation Example

M. N. Feller and I. I. Kovtun, Quasilinear parabolic equations with a Lévy Laplacian for functions of infinite number of variables, Methods Funct. Anal. Topology 14 (2008), no. 2, 117-123.

BibTex

@article {MFAT449,
AUTHOR = {Feller, M. N. and Kovtun, I. I.},
TITLE = {Quasilinear parabolic equations with a Lévy Laplacian for functions of infinite number of variables},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {14},
YEAR = {2008},
NUMBER = {2},
PAGES = {117-123},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=449},
}