We prove a theorem on the well-posedness of the Cauchy problem for a linear higher-order stochastic equation of parabolic type with time-dependent coefficients and continuous perturbations whose solutions are subjected to pulse action at fixed times.
Similar content being viewed by others
References
A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).
I. I. Gikhman, “Boundary-value problem for a stochastic equation of parabolic type,” Ukr. Mat. Zh., 31, No. 5, 483–489 (1979).
Il. I. Gikhman, “On a mixed problem for a stochastic differential equation of parabolic type,” Ukr. Mat. Zh., 32, No. 3, 367–372 (1980).
A. Ya. Dorogovtsev, S. D. Ivasishen, and A. G. Kukush,” Asymptotic behavior of solutions of the heat equation with white noise on its right-hand side,” Ukr. Mat. Zh., 57, No. 1, 13–20 (1985).
N. A. Perestyuk and A. V. Tkach, “Periodic solutions of weakly nonlinear impulsive systems of partial differential equations,” Ukr. Mat. Zh., 43, No. 4, 601–605 (1997).
M. I. Matiichuk and V. M. Luchko, “Cauchy problem for parabolic systems with pulse action,” Ukr. Mat. Zh., 58, No. 11, 323–335 (2006).
S. D. Éidel’man, Parabolic Systems [in Russian], Nauka, Moscow (1964).
M. L. Sverdan, E. F. Tsarkov, and V. K. Yasyns’kyi, Stochastic Dynamical Systems with Finite Aftereffect [in Ukrainian], Zelena Bukovyna, Chernivtsi (2000).
I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes [in Russian], Nauka, Moscow (1977).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1422–1426, October, 2008.
Rights and permissions
About this article
Cite this article
Perun, H.M. Problem with pulse action for a linear stochastic parabolic equation of higher order. Ukr Math J 60, 1660–1665 (2008). https://doi.org/10.1007/s11253-009-0151-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-009-0151-y