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# Boundary problems and initial-boundary value problems for one class of nonlinear parabolic equations with Lévy Laplacian

### Abstract

We develop a method to construct a solution to a boundary problem and an initial-boundary value problem in a fundamental domain of a Hilbert space for a class of nonlinear parabolic equations not containing explicitly the unknown function, $$\frac{\partial U(t,x)}{\partial t}=f(t,\Delta_LU(t,x)),$$ where $\Delta _L$ is the infinite dimensional Lévy Laplacian.

### Article Information

 Title Boundary problems and initial-boundary value problems for one class of nonlinear parabolic equations with Lévy Laplacian Source Methods Funct. Anal. Topology, Vol. 17 (2011), no. 2, 118-125 MathSciNet MR2849472 Copyright The Author(s) 2011 (CC BY-SA)

### Authors Information

M. N. Feller
UkrNII Resurs'', 84 Bozhenko, Kyiv, 03150, Ukraine

I. I. Kovtun
National University of Life and Environmental Sciences of Ukraine, 15 Geroiv Oborony, Kyiv, 03041, Ukraine

### Citation Example

M. N. Feller and I. I. Kovtun, Boundary problems and initial-boundary value problems for one class of nonlinear parabolic equations with Lévy Laplacian, Methods Funct. Anal. Topology 17 (2011), no. 2, 118-125.

### BibTex

@article {MFAT531,
AUTHOR = {Feller, M. N. and Kovtun, I. I.},
TITLE = {Boundary problems and initial-boundary value problems for one class of nonlinear parabolic equations with Lévy Laplacian},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {17},
YEAR = {2011},
NUMBER = {2},
PAGES = {118-125},
ISSN = {1029-3531},
MRNUMBER = {MR2849472},
URL = {http://mfat.imath.kiev.ua/article/?id=531},
}