Problem with pulse action for systems with Bessel–Kolmogorov operators
- M. I. Konarovs’ka
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We construct the fundamental matrix of solutions of the Cauchy problem and a problem with pulse action for systems with Bessel–Kolmogorov operators degenerate in all space variables. Estimates for the fundamental matrix are obtained, and its properties are established.
- S. D. Eidelman, S. D. Ivasyshen, and A. N. Kochubei, Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type, Birkhäuser, Basel (2004). CrossRef
- S. Polidoro, “On a class of ultraparabolic operators of Kolmogorov–Fokker–Planck type,” Matematiche, 49, No. 1, 53–105 (1994).
- M. Di Francesco and S. Polidoro, “On a class of degenerate parabolic equation of Kolmogorov type,” AMRX Appl. Math. Res. Express., No. 3, 77–116 (2005).
- H. P. Malyt’ska, “On the fundamental solution of the Cauchy problem for a parabolic equation of the Kolmogorov type of arbitrary order degenerate in an arbitrary number of groups of variables,” Mat. Met. Fiz.-Mekh. Polya, 47, No. 4, 131–138 (2004).
- H. P. Malyt’ska, “Systems of equations of Kolmogorov type,” Ukr. Mat. Zh., 60, No. 12, 1650–1663 (2008); English translation: Ukr. Math. J., 60, No. 12, 1937–1954 (2008). CrossRef
- L. M. Ivasishen, Integral Representation and Sets of Initial Values of Solutions of Parabolic Equations with Bessel Operator and Increasing Coefficients [in Russian], Dep. in UkrINT ÉI, No. 1731-Uk.92, Chernovtsy (1992).
- T. M. Balabushenko, S. D. Ivasyshen, V. P. Lavrenchuk, and L. M. Mel’nychuk, “Fundamental solution of the Cauchy problem for some parabolic equations with Bessel operator and increasing coefficients,” Nauk. Visn. Cherniv. Univ., Ser. Mat., Issue 288, 5–11 (2006).
- A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).
- N. A. Perestyuk, V. A. Plotnikov, A. M. Samoilenko, and N. V. Skripnik, Differential Equations with Impulse Effects: Multivalued Right-Hand Sides with Discontinuities, de Gruyter, Berlin (2011). CrossRef
- A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore (1995).
- B. G. Korenev, An Introduction to the Theory of Bessel Functions [in Russian], Nauka, Moscow (1971).
- R. Courant, Partial Differential Equations [Russian translation], Mir, Moscow (1964).
- S. D. Éidel’man, Parabolic Systems [in Russian], Nauka, Moscow (1964).
- M. I. Matiichuk, Parabolic Singular Boundary-Value Problems [in Ukrainian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (1999).
- Problem with pulse action for systems with Bessel–Kolmogorov operators
Ukrainian Mathematical Journal
Volume 64, Issue 7 , pp 1078-1089
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- 1. Chernivtsi National University, Chernivtsi, Ukraine