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.

Full Text

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},
}