Electron. J. Differential Equations, Vol. 2018 (2018), No. 128, pp. 1-10.

Multipoint initial-final value problems for dynamical Sobolev-type equations in the space of noises

Angelo Favini, Sophiya A. Zagrebina, Georgy A. Sviridyuk

Abstract:
We prove the existence of a unique solution for a linear stochastic Sobolev-type equation with a relatively p-bounded operator and a multipoint initial-final condition, in the space of ``noises''. We apply the abstract results to specific multipoint initial-final and boundary value problems for the linear Hoff equation which models I-beam bulging under random load.

Submitted March 6, 2018. Published June 19, 2018.
Math Subject Classifications: 60H30, 34K50, 34M99.
Key Words: Dynamical Sobolev-type equation; Wiener K-process; multipoint initial-final conditions; Nelson-Gliklikh derivative;white noise; space of noises; stochastic Hoff equation

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Angelo Favini
Department of Mathematics
Bologna University
Piazza di Porta San Donato 5, 40126
Bologna (BO), Italy
email: angelo.favini@unibo.it
Sophiya A. Zagrebina
Department of Mathematical and Computer Modelling
South Ural State University, Lenin av., 76
Chelyabinsk, 454080, Russian Federation
email: zagrebinasa@susu.ru
Georgy A. Sviridyuk
Department of Mathematical Physics Equations
South Ural State University, Lenin av., 76
Chelyabinsk, 454080, Russian Federation
email: sviridyuk@susu.ru

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