On applications of the Levi method in the theory of parabolic equations
Journal Title: Математичні Студії - Year 2017, Vol 47, Issue 1
Abstract
A short review of papers where a fundamental solution was constructed by the Levi’s parametrix method is done. Some details of applications of this method for parabolic equations and systems of parabolic equations, in particular the procedure of constructing a parametrix for equations with different degenerations and singularities, are considered. The basic results of constructing of a fundamental solution for degenerate ultraparabolic equations of the Kolmogorov type by the Levi paramerix method under different assumptions on the coefficients are reviewed. Some new authors’ results on the constructing of a classical fundamental solution and, so-called, L-fundamental solution for the equation with coefficients with two groups of spatial variables are presented. These results are obtained by stepwise using of the Levi parametrix method and special Holder conditions on the coefficients.
Authors and Affiliations
S. D. Ivasyshen, I. P. Medynsky
Keywords
Related Articles
- EP ID EP310039
- DOI 10.15330/ms.47.1.33-46
- Views 52
- Downloads 0
Polynomial complex Ginzburg-Landau equations in Zhidkov spaces
We consider the so-called Complex Ginzburg-Landau equations with a polynomial nonlin- earity in the real line. We prove existence results concerned with the initial value problem for these equations in Zhidkov spaces wit...
On the transcendental meromorphic solutions of a certain class of differential equations
In this paper we consider the differential equation F(k)−a2=eγ{α(F−a1)+β}, where ai(z),α(z)(≢0,∞), β(z)(≢∞), i=1,2 are small functions of F, γ is an entire function and k∈N. Let f be a transcendental meromorphic functi...
On one variational problem reducing to differential-boundary operator
One quadratic functional in the real space L2(Ω)(Ω⊂R2) is considered. The conditions are being necessary for the finding of its minimum are indicated and the problem of finding of corresponding sufficient conditions is f...
A note on bornologies
A bornology on a set X is a family B of subsets of X closed under taking subsets, finite unions and such that ⋃B=X. We prove that, for a bornology B on X, the following statements are equivalent: (1) there exists a vecto...
Fast growing meromorphic solutions of the systems of linear differential equations
Systems of linear differential equations that allow for dimension decrease are considered. Growth estimates for meromorphic vector-solutions are obtained. An essentially new feature is that there are no additional constr...