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

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.

Keywords

• Dynamical Sobolev-type equation
• Wiener K-process
• multipoint initial-final conditions
• Nelson-Gliklikh derivative
• hite noise
• space of noises
• stochastic Hoff equation