Properties of fundamental solutions, correct solvability of the Cauchy problem and integral representations of solutions for ultraparabolic Kolmogorov–type equations with three groups of spatial variables and with degeneration on the initial hyperplane
| dc.citation.epage | 790 | |
| dc.citation.issue | 3 | |
| dc.citation.journalTitle | Математичне моделювання та комп'ютинг | |
| dc.citation.spage | 779 | |
| dc.contributor.affiliation | Західноукраїнський національний університет | |
| dc.contributor.affiliation | Інститут прикладних проблем механіки і метематики ім. Я. С. Підстригача НАН України | |
| dc.contributor.affiliation | Національний університет “Львівська політехніка” | |
| dc.contributor.affiliation | West Ukrainian National University | |
| dc.contributor.affiliation | Pidstryhach Institute for Applied Problems of Mechanics and Mathematics | |
| dc.contributor.affiliation | Lviv Polytechnic National University | |
| dc.contributor.author | Возняк, О. Г. | |
| dc.contributor.author | Дронь, В. С. | |
| dc.contributor.author | Мединський, І. П. | |
| dc.contributor.author | Voznyak, O. G. | |
| dc.contributor.author | Dron, V. S. | |
| dc.contributor.author | Medynskyi, I. P. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-03-04T11:33:04Z | |
| dc.date.created | 2022-02-28 | |
| dc.date.issued | 2022-02-28 | |
| dc.description.abstract | Для однорідного ультрапараболічного рівняння типу Колмогорова з трьома групами просторових змінних (в т.ч. двома групами просторових змінних виродження) і виродженням на початковій гіперплощині встановлено деякі властивості фундаментального розв’язку задачі Коші. Для всіх випадків виродження на початковій гіперплощині доведено теореми про інтегральні зображення розв’язків і коректну розв’язність задачі Коші в класах вагових функцій. Для рівнянь з указаного класу ці результати є новими. | |
| dc.description.abstract | Some properties of the fundamental solution of the Cauchy problem for homogeneous ultraparabolic Kolmogorov–type equation with three groups of spatial variables including two groups of degeneration and with degeneration on the initial hyperplane are established. For different type of degeneration on the initial hyperplane the theorems on integral representations of solutions and correct solvability of the Cauchy problem are presented. These results for such type of equations are obtained in appropriate classes of weight functions. | |
| dc.format.extent | 779-790 | |
| dc.format.pages | 12 | |
| dc.identifier.citation | Voznyak O. G. Properties of fundamental solutions, correct solvability of the Cauchy problem and integral representations of solutions for ultraparabolic Kolmogorov–type equations with three groups of spatial variables and with degeneration on the initial hyperplane / O. G. Voznyak, V. S. Dron, I. P. Medynskyi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 3. — P. 779–790. | |
| dc.identifier.citationen | Voznyak O. G. Properties of fundamental solutions, correct solvability of the Cauchy problem and integral representations of solutions for ultraparabolic Kolmogorov–type equations with three groups of spatial variables and with degeneration on the initial hyperplane / O. G. Voznyak, V. S. Dron, I. P. Medynskyi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 3. — P. 779–790. | |
| dc.identifier.doi | doi.org/10.23939/mmc2022.03.779 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/63474 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та комп'ютинг, 3 (9), 2022 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 3 (9), 2022 | |
| dc.relation.references | [1] Kolmogoroff A. N. Zuf¨allige Bevegungen (Zur Theorie der Brownshen Bewegung). Annals of Mathematics. 35 (1), 116–117 (1934). | |
| dc.relation.references | [2] Protsakh N. P., Ptashnyk B. Yo. Nonlinear ultraparabolic equations and variational inequalities. Naukova Dumka, Kyiv (2017), (in Ukrainian). | |
| dc.relation.references | [3] Citti G., Pascucci A., Polidoro S. On the regularity of solutions to a nonlinear ultraparabolic equations arising in mathematical finance. Differential and Integral Equations. 14 (6), 701–738 (2001). | |
| dc.relation.references | [4] Di Franchesco M., Pascucci A. On a class of degenerate parabolic equations of Kolmogorov type. Applied Mathematics Research eXpress. 2005 (6), 77–116 (2005). | |
| dc.relation.references | [5] Di Franchesco M., Pascucci A. A continuous dependence result for ultraparabolic equations in option pricing. Journal of Mathematical Analysis and Applications. 336 (2), 1026–1041 (2007). | |
| dc.relation.references | [6] Foschi P., Pascucci A. Kolmogorov equations arising in finance: direct and inverse problem. Lecture notes of Seminario Interdisciplinare di Matematica. Universita delgi studi della Basilicata. 1, 145–156 (2007). | |
| dc.relation.references | [7] Ivashyshen S. D., Medynsky I. P. The Fokker–Planck–Kolmogorov equations for some degenerate diffusion processes. Theory of Stochastic Processes. 16(32) (1), 57–66 (2010). | |
| dc.relation.references | [8] Lanconelli E., Pascucci A. On a class of hypoelliptic evolution equations. Rend. Sem. Mat. Univ. Politec. Torino. 52 (1), 29–63 (1994). | |
| dc.relation.references | [9] Pascucci A. Kolmogorov equations in physics and finance. Progress in Nonlinear Differential Equations and Their Applications. 63, 313–324 (2005). | |
| dc.relation.references | [10] Polidoro S. A Global Lower Bound for the Fundamental Solution of Kolmogorov–Fokker–Planck Equations. Archive for Rational Mechanics and Analysis. 137, 321–340 (1997). | |
| dc.relation.references | [11] Eidelman S. D., Kochubei A. N., Ivasyshen S. D. Analytic methods in the theory of differential and pseudodifferential equations of parabolic type. Operator Theory: Advances and Applications. 152. Birkhauser, Basel (2004). | |
| dc.relation.references | [12] Ivashyshen S. D., Medynsky I. P. On applications of the Levi method in the theory of parabolic equations. Matematychni Studii. 47 (1), 33–46 (2017). | |
| dc.relation.references | [13] Ivashyshen S. D., Medynsky I. P. The classical fundamental solution of a degenerate Kolmogorov’s equation with coefficients independent on variables of degeneration. Bukovinian Mathematical Journal. 2 (2–3), 94–106 (2014), (in Ukrainian). | |
| dc.relation.references | [14] Ivasyshen S. D., Medyns’kyi I. P. Classical fundamental solutions of the Cauchy problem for ultraparabolic equations of Kolmogorov type with two groups of spatial variables. Diff. equations and related topics. Proceedings of Institute of Mathematics NAS of Ukraine. 13 (1), 108–155 (2016), (in Ukrainian). | |
| dc.relation.references | [15] Ivasyshen S. D., Medyns’kyi I. P. On the classical fundamental solutions of the Cauchy problem for ultraparabolic Kolmogorov–type equations with two groups of spatial variables. Journal of Mathematical Sciences. 231 (4), 507–526 (2018). | |
| dc.relation.references | [16] Ivasyshen S. D., Medyns’kyi I. P. Classical fundamental solution of the Cauchy problem for ultraparabolic Kolmogorov–type equations with two qroups of spatial variables of degeneration. I. Journal of Mathematical Sciences. 246 (2), 121–151 (2020). | |
| dc.relation.references | [17] Ivasyshen S. D., Medyns’kyi I. P. Classical fundamental solution of the Cauchy problem for ultraparabolic Kolmogorov–type equations with two qroups of spatial variables of degeneration. II. Journal of Mathematical Sciences. 247 (1), 1–23 (2020). | |
| dc.relation.references | [18] Voznyak O. G., Ivashyshen S. D., Medynsky I. P. On fundamental solution of the Cauchy problem for ultraparabolic Kolmogorov’s equation with degeneration on the initial hyperplane. Bukovinian Mathematical Journal. 3 (3–4), 41–51 (2015), (in Ukrainian). | |
| dc.relation.referencesen | [1] Kolmogoroff A. N. Zuf¨allige Bevegungen (Zur Theorie der Brownshen Bewegung). Annals of Mathematics. 35 (1), 116–117 (1934). | |
| dc.relation.referencesen | [2] Protsakh N. P., Ptashnyk B. Yo. Nonlinear ultraparabolic equations and variational inequalities. Naukova Dumka, Kyiv (2017), (in Ukrainian). | |
| dc.relation.referencesen | [3] Citti G., Pascucci A., Polidoro S. On the regularity of solutions to a nonlinear ultraparabolic equations arising in mathematical finance. Differential and Integral Equations. 14 (6), 701–738 (2001). | |
| dc.relation.referencesen | [4] Di Franchesco M., Pascucci A. On a class of degenerate parabolic equations of Kolmogorov type. Applied Mathematics Research eXpress. 2005 (6), 77–116 (2005). | |
| dc.relation.referencesen | [5] Di Franchesco M., Pascucci A. A continuous dependence result for ultraparabolic equations in option pricing. Journal of Mathematical Analysis and Applications. 336 (2), 1026–1041 (2007). | |
| dc.relation.referencesen | [6] Foschi P., Pascucci A. Kolmogorov equations arising in finance: direct and inverse problem. Lecture notes of Seminario Interdisciplinare di Matematica. Universita delgi studi della Basilicata. 1, 145–156 (2007). | |
| dc.relation.referencesen | [7] Ivashyshen S. D., Medynsky I. P. The Fokker–Planck–Kolmogorov equations for some degenerate diffusion processes. Theory of Stochastic Processes. 16(32) (1), 57–66 (2010). | |
| dc.relation.referencesen | [8] Lanconelli E., Pascucci A. On a class of hypoelliptic evolution equations. Rend. Sem. Mat. Univ. Politec. Torino. 52 (1), 29–63 (1994). | |
| dc.relation.referencesen | [9] Pascucci A. Kolmogorov equations in physics and finance. Progress in Nonlinear Differential Equations and Their Applications. 63, 313–324 (2005). | |
| dc.relation.referencesen | [10] Polidoro S. A Global Lower Bound for the Fundamental Solution of Kolmogorov–Fokker–Planck Equations. Archive for Rational Mechanics and Analysis. 137, 321–340 (1997). | |
| dc.relation.referencesen | [11] Eidelman S. D., Kochubei A. N., Ivasyshen S. D. Analytic methods in the theory of differential and pseudodifferential equations of parabolic type. Operator Theory: Advances and Applications. 152. Birkhauser, Basel (2004). | |
| dc.relation.referencesen | [12] Ivashyshen S. D., Medynsky I. P. On applications of the Levi method in the theory of parabolic equations. Matematychni Studii. 47 (1), 33–46 (2017). | |
| dc.relation.referencesen | [13] Ivashyshen S. D., Medynsky I. P. The classical fundamental solution of a degenerate Kolmogorov’s equation with coefficients independent on variables of degeneration. Bukovinian Mathematical Journal. 2 (2–3), 94–106 (2014), (in Ukrainian). | |
| dc.relation.referencesen | [14] Ivasyshen S. D., Medyns’kyi I. P. Classical fundamental solutions of the Cauchy problem for ultraparabolic equations of Kolmogorov type with two groups of spatial variables. Diff. equations and related topics. Proceedings of Institute of Mathematics NAS of Ukraine. 13 (1), 108–155 (2016), (in Ukrainian). | |
| dc.relation.referencesen | [15] Ivasyshen S. D., Medyns’kyi I. P. On the classical fundamental solutions of the Cauchy problem for ultraparabolic Kolmogorov–type equations with two groups of spatial variables. Journal of Mathematical Sciences. 231 (4), 507–526 (2018). | |
| dc.relation.referencesen | [16] Ivasyshen S. D., Medyns’kyi I. P. Classical fundamental solution of the Cauchy problem for ultraparabolic Kolmogorov–type equations with two qroups of spatial variables of degeneration. I. Journal of Mathematical Sciences. 246 (2), 121–151 (2020). | |
| dc.relation.referencesen | [17] Ivasyshen S. D., Medyns’kyi I. P. Classical fundamental solution of the Cauchy problem for ultraparabolic Kolmogorov–type equations with two qroups of spatial variables of degeneration. II. Journal of Mathematical Sciences. 247 (1), 1–23 (2020). | |
| dc.relation.referencesen | [18] Voznyak O. G., Ivashyshen S. D., Medynsky I. P. On fundamental solution of the Cauchy problem for ultraparabolic Kolmogorov’s equation with degeneration on the initial hyperplane. Bukovinian Mathematical Journal. 3 (3–4), 41–51 (2015), (in Ukrainian). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2022 | |
| dc.subject | ультрапараболічне рівняння типу Колмогорова | |
| dc.subject | виродження на початковій гіперплощині | |
| dc.subject | фундаментальний розв’язок задачі Коші | |
| dc.subject | вагові простори | |
| dc.subject | інтегральні зображення розв’язків | |
| dc.subject | коректна розв’язність задачі Коші | |
| dc.subject | ultraparabolic equations of the Kolmogorov type | |
| dc.subject | fundamental solution of the Cauchy problem | |
| dc.subject | weight spaces | |
| dc.subject | integral representations of solutions | |
| dc.subject | correct solvability of the Cauchy problem | |
| dc.title | Properties of fundamental solutions, correct solvability of the Cauchy problem and integral representations of solutions for ultraparabolic Kolmogorov–type equations with three groups of spatial variables and with degeneration on the initial hyperplane | |
| dc.title.alternative | Властивості фундаментальних розв’язків, коректна розв’язність задачі Коші та інтегральні зображення розв’язків для ультрапараболічних рівнянь типу Колмогорова з трьома групами просторових змінних та виродженням на початковій гіперплощині | |
| dc.type | Article |
Files
License bundle
1 - 1 of 1