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# 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},
MRNUMBER = {MR2432760},
URL = {http://mfat.imath.kiev.ua/article/?id=449},
}