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

Multipoint initial-final value problems for dynamical Sobolev-type equations in the space of noises. (English) Zbl 1434.60139

Electron. J. Differ. Equ. 2018, Paper No. 128, 10 p. (2018).
Summary: 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.

Cited in 23 Documents

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34K50 Stochastic functional-differential equations
60H30 Applications of stochastic analysis (to PDEs, etc.)
60H40 White noise theory
47A10 Spectrum, resolvent

Keywords:

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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References:

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