Zobrazeno 1 - 10
of 18
pro vyhledávání: '"Krzysztof A. Topolski"'
Autor:
Krzysztof A. Topolski
Publikováno v:
Electronic Journal of Differential Equations, Vol 2015, Iss 113,, Pp 1-12 (2015)
We consider the initial value problem for degenerate parabolic equations. We prove theorems on differential inequalities and comparison theorems in unbounded domain. As a solution of differential inequality we consider upper absolutely (lower abso
Externí odkaz:
https://doaj.org/article/ee218920f96a479ab640ae428bd5b6f3
Autor:
Krzysztof A. Topolski
Publikováno v:
Opuscula Mathematica, Vol 34, Iss 2, Pp 425-441 (2014)
The degenerate parabolic Cauchy problem is considered. A functional argument in the equation is of the Hale type. As a limit of piecewise classical solutions we obtain a viscosity solution of the main problem. Presented method is an adaptation of Ton
Externí odkaz:
https://doaj.org/article/8efb2796a6564ea18577f06377335620
Autor:
Krzysztof A. Topolski
Publikováno v:
Abstract and Applied Analysis, Vol 2015 (2015)
We present a counterexample to the main result of the abovementioned paper showing that this result is false and cannot be improved in a simple way.
Externí odkaz:
https://doaj.org/article/7fd6e066a486476fbb34e6e1fb302406
Autor:
Krzysztof A. Topolski
Publikováno v:
Abstract and Applied Analysis, Vol 3, Iss 3-4, Pp 363-375 (1998)
We consider the initial-boundary value problem for second order differential-functional equations of parabolic type. Functional dependence in the equation is of the Hale type. By using Leray-Schauder theorem we prove the existence of classical soluti
Externí odkaz:
https://doaj.org/article/bdfcf71228c5441290bcff57117ed1c0
Publikováno v:
Applied Mathematics and Computation. 343:156-166
We study a kinetic equation which describes self-organization of various complex systems, assuming the interacting rate with small support. This corresponds to interactions between an agent with a given internal state and agents having short distance
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3f5448b866ee92bda2823591abe4858c
https://doi.org/10.1016/j.amc.2018.09.050
https://doi.org/10.1016/j.amc.2018.09.050
Publikováno v:
Applied Mathematics and Computation. 417:126778
In the present paper we study Euler–type approximations along characteristics for a class of kinetic equations that describe swarm formations in the case when the interactions rate is variable. The proposed numerical schemes preserve essential prop
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b47643cdfccdb8cf197505cd66d86029
https://doi.org/10.1016/j.amc.2021.126778
https://doi.org/10.1016/j.amc.2021.126778
Autor:
Krzysztof A. Topolski
Publikováno v:
Annales Polonici Mathematici. 113:269-282
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::733241cd912ed36991c2892463a6b70e
https://doi.org/10.4064/ap113-3-4
https://doi.org/10.4064/ap113-3-4
On the numerical approximation of viscosity solutions for the differential-functional Cauchy problem
Autor:
Krzysztof A. Topolski
Publikováno v:
Calcolo. 50:329-343
We consider the Cauchy problem for first order differential-functional equations. We present finite difference schemes to approximate viscosity solutions of this problem. The functional dependence in the equation is of the Hale type. It contains, as
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bc2098666619b186e128f4c503853f65
https://doi.org/10.1007/s10092-012-0071-3
https://doi.org/10.1007/s10092-012-0071-3
Autor:
Krzysztof A. Topolski
Publikováno v:
Acta Mathematica Hungarica. 129:277-296
We consider the nonlinear Cauchy problem for second order differential-functional equations of parabolic type, and present two existence theorems: in the class of bounded and in the class of unbounded viscosity solutions. These are based on different
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a28f6b1bed971783d30e56be6300bb61
https://doi.org/10.1007/s10474-010-0029-3
https://doi.org/10.1007/s10474-010-0029-3
Autor:
Krzysztof A. Topolski
Publikováno v:
Czechoslovak Mathematical Journal. 58:927-947
We consider the initial-boundary value problem for first order differential-functional equations. We present the ‘vanishing viscosity’ method in order to obtain viscosity solutions. Our formulation includes problems with a retarded and deviated a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c816776ebcb101a03695c4150bff238c
https://doi.org/10.1007/s10587-008-0061-4
https://doi.org/10.1007/s10587-008-0061-4