On Feller semigroup generated by solution of nonlocal parabolic conjugation problem
Journal Title: Карпатські математичні публікації - Year 2018, Vol 10, Issue 2
Abstract
The paper deals with the problem of construction of Feller semigroup for one-dimensional inhomogeneous diffusion processes with membrane placed at a point whose position on the real line is determined by a given function that depends on the time variable. It is assumed that in the inner points of the half-lines separated by a membrane the desired process must coincide with the ordinary diffusion processes given there, and its behavior on the common boundary of these regions is determined by the nonlocal conjugation condition of Feller-Wentzell's type. This problem is often called a problem of pasting together two diffusion processes on a line. In order to study the described problem we use analytical methods. Such an approach allows us to determine the desired operator family using the solution of the corresponding problem of conjugation for a linear parabolic equation of the second order (the Kolmogorov backward equation) with discontinuous coefficients. This solution is constructed by the boundary integral equations method under the assumption that the coefficients of the equation satisfy the Holder condition with a nonzero exponent, the initial function is bounded and continuous on the whole real line, and the parameters characterizing the Feller-Wentzell conjugation condition and the curve defining the common boundary of the domains, where the equation is given, satisfies the Holder condition with exponent greater than 12.
Authors and Affiliations
B. I. Kopytko, R. V. Shevchuk
Keywords
Related Articles
- EP ID EP535461
- DOI 10.15330/cmp.10.2.333-345
- Views 54
- Downloads 0
Some fixed point results in complete generalized metric spaces
The Banach contraction principle is the important result, that has many applications. Some authors\- were interested in this principle in various metric spaces. Branciari A. initiated the notion of the generalized metric...
The convergence classes for analytic functions in the Reinhardt domains
Let L0 be the class of positive increasing on [1,+∞) functions l such that l((1+o(1))x)=(1+o(1))l(x) (x→+∞). We assume that α is a concave function such that α(ex)∈L0 and function β∈L0 such that ∫+∞1α(x)/β(x)dx<+∞. In th...
A Worpitzky boundary theorem for branched continued fractions of the special form
For a branched continued fraction of a special form we propose the limit value set for the Worpitzky-like theorem when the element set of the branched continued fraction is replaced by its boundary.
On some perturbations of a stable process and solutions to the Cauchy problem for a class of pseudo-differential equations
A fundamental solution for some class of pseudo-differential equations is constructed by the method based on the theory of perturbations. We consider a symmetric α-stable process in multidimensional Euclidean space. Its...
On the intersection of weighted Hardy spaces
Let $H^p_\sigma( \mathbb{C}_+)$, $1\leq p <+\infty$, $0\leq \sigma < +\infty$, be the space of all functions f analytic in the half plane $\mathbb{C}_{+}= \{ z: \text {Re} z>0 \}$ and such that $$ \|f\|:=\sup\limits_{...