Investigation of the Cauchy problem for stochastic partial differential equations
It is shown that the solutions of stochastic linear parabolic equations with Poisson perturbations are stabilized in the mean square. The problem of determining the reserve of stability for a rod under random perturbations is studied.
Збережено в:
| Дата: | 1993 |
|---|---|
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1993
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5928 |
| Теги: |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512150216245248 |
|---|---|
| author | Perun, H. M. Yasinsky, V. K. Перун, Г. М. Ясинский, В. К. Перун, Г. М. Ясинский, В. К. |
| author_facet | Perun, H. M. Yasinsky, V. K. Перун, Г. М. Ясинский, В. К. Перун, Г. М. Ясинский, В. К. |
| author_sort | Perun, H. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:21:13Z |
| description | It is shown that the solutions of stochastic linear parabolic equations with Poisson perturbations are stabilized in the mean square. The problem of determining the reserve of stability for a rod under random perturbations is studied. |
| first_indexed | 2026-03-24T03:24:12Z |
| format | Article |
| fulltext |
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It is found that the solutions of stochastic linear parabolic equations with Poisson perturbations are
stabilized in square mean. The problem of detennining the stability margin of a rod under random per
turbations is studied.
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= [ Q( C, ;, • ! )u(t, x. CO) ]u(t, CO)+
+ l[ Q( G, ;,. r y<v)u(t,x,CO) ]v(dv,t), (1)
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ISSN 0041-(,()53. YKp. Mam. ;,rypn., 1993, m. 45, N" 9
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ISSN 0041-{,<}53. Y,q,. >tam. xyp1e., 1993. m. 45. NV 9
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ISSN 004/-6053. Y,q, . Mam. JKJpn,, 1993, m. 45, N" 9
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I
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0
r,ne K = K 1 + K2 , L = L 1 + L 2• Ilo JieMMe f'pouyoJIJia [4] HMeeM
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dt V V
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2
Z(s,ia)ds.
(10)
(11)
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dt 'I{ V dt '
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= _l_ •s I Q(C, i'A, iCJ)i2 cIA, +
2n -~ IP(iA., iCJ)i2
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ISSN 0041-6053. YKp. Mam. )l(YP"· · 1993, 111. 45, N• 9
(12)
1264 r . M . IIEPYH, B. K. RCI-IHCKl-ftt
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I ➔~
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~ ~ ~2
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du(0, x)
u(0, x) = /1 (x); dt = fz(x). (14)
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no napaMerpaM akiki . O6o3nat:t:HM
m
P('A, cr) = L ak1k2').__k1(icrf2.
k=O .
ISSN 0041-6053 . YKp. Mam. )l(JP"· · 1993, m . 45, N• 9
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[
l ~ 111l1 1cr1k2 ]- 1
Sk k = sup - f ---- QA
1 2 cr 2rr - ~ IP(1A, cr)I
(15)
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l. Tu.xMaH HA. H., Mecme«KuHa T. M. 3ana<Ja K ow11 llJJJI napa60J111<JecKoro ypastteHHJI c K03<pq}H
UHeHTaMH THna "6em,1A wyM" // TeopHJ1 cny<JaAH. npoueccos. - 1987. - 81,m. 15. - C . 19 - 28.
2. r,a~Ullt H. H . CToxaCTll'lCCKHC l~Hq><pepeHUHaJJbHble ypaBHeHHJI C 'l3CTHblMII npoH3B0/lHblMH //
K a <JeCTBCHHble MCT0/lbl II HCCJIC/l0BaHHJI HeJJHHCAH. llllq><pepeHu. ypaBI-ICHIIA II HCJIHHCAH. K0JJe-
6attHA. - KHeB: 11H-T MaTeMaTHKH AH YCCP, 1981. - C. 25 - 59.
3. Tu.xM£111 H . H., CKopoxoo A. B. CToxacT11<JecK11e n11qxpepettu11a;11,tt1,1e ypaBHCHIIJI H HX npHJJ0-
)KCHH.ll. - KHeB: HayK. llYMKa, 1982. - 612 c .
4. Tu.xMaH H . H ., CKopoxoo A. B. CToxacT11'lecK11c n11cpq>epe ttu11an1,111,1e ypaBHCHHJI. - K11eB:
HayK. llYMKa, 1968. - 354 c.
5. flc1t1U:Ka.R JI. H. , flcw<CKltll B. K. ACIIMIIT0Tll'ICCKaJI ycT0A'lHBOCTb B cpenHeM KBanpaTH'IH0M
TpllBllaJJbH0ro peweHHJI CT0XaCTH'lCCKOl-o cpyttKUHOHaJJbtlO-llHq><pepeHUHaJJbHOro ypaBHCHll.ll .//
YKp. MaT. )KypH. - 1980. - 32, N" l. - C. 89 - 98.
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MYll.lCHHJIX HX napaMCTpoB. - M.: HayKa, 1969. - 367 C.
7. Cao06.RK A. M ., I.{apbKOO E. <P. MaTpHua K o wH CIICTCMbl JI HHCJ.lHblX CT0XaCTH'lC-CKHX n11¢q>e
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0HaJJbHble ypaBHCHHJI. - P11ra: OPT, 1992. - 331 C.
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Tiony<JeHo 26.11.91
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| id | umjimathkievua-article-5928 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:24:12Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/d6/b77e3fff8bd144c66e5aaabb5f2554d6.pdf |
| spelling | umjimathkievua-article-59282020-03-19T09:21:13Z Investigation of the Cauchy problem for stochastic partial differential equations Исследование задачи Коши для стохастических уравнений в частных производны Perun, H. M. Yasinsky, V. K. Перун, Г. М. Ясинский, В. К. Перун, Г. М. Ясинский, В. К. It is shown that the solutions of stochastic linear parabolic equations with Poisson perturbations are stabilized in the mean square. The problem of determining the reserve of stability for a rod under random perturbations is studied. Встановлена стабілізація в середньому квадратичному розв’язків стохастичних лінійних рівнянь параболічного типу з пуассоновими збуреннями та розглянута задача визначення запасу стійкості стержня під дією випадкових збурень. Institute of Mathematics, NAS of Ukraine 1993-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5928 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 9 (1993); 1259–1265 Український математичний журнал; Том 45 № 9 (1993); 1259–1265 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5928/8539 https://umj.imath.kiev.ua/index.php/umj/article/view/5928/8540 Copyright (c) 1993 Perun H. M.; Yasinsky V. K. |
| spellingShingle | Perun, H. M. Yasinsky, V. K. Перун, Г. М. Ясинский, В. К. Перун, Г. М. Ясинский, В. К. Investigation of the Cauchy problem for stochastic partial differential equations |
| title | Investigation of the Cauchy problem for stochastic partial differential equations |
| title_alt | Исследование задачи Коши для стохастических уравнений в частных производны |
| title_full | Investigation of the Cauchy problem for stochastic partial differential equations |
| title_fullStr | Investigation of the Cauchy problem for stochastic partial differential equations |
| title_full_unstemmed | Investigation of the Cauchy problem for stochastic partial differential equations |
| title_short | Investigation of the Cauchy problem for stochastic partial differential equations |
| title_sort | investigation of the cauchy problem for stochastic partial differential equations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5928 |
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