Time-dependent operator matrices and inhomogeneous Cauchy problems

1998 ◽  
Vol 47 (1) ◽  
pp. 5-24
Author(s):  
Nguyen Thanh Lan ◽  
Gregor Nickel
Keyword(s):  
Time Dependent ◽  
Cauchy Problems ◽  
Operator Matrices

Moments of certain stochastic integrals occurring in mathematical physics

1992 ◽  
Vol 120 (3-4) ◽  
pp. 267-282 ◽  
Author(s):  
Lieven Smits
Keyword(s):  
Brownian Motion ◽  
Vector Field ◽  
Mathematical Physics ◽  
Time Dependent ◽  
Regularity Conditions ◽  
Stochastic Integrals ◽  
Cauchy Problems ◽  
Dependent Vector ◽  
Set Up

SynopsisWe give an expression for the n-th moment of certain Itô integrals. The integrands considered are nonanticipating functionals of the form s↦a(s, Xs), where a is a measurable time-dependent vector field in space satisfying mild regularity conditions, and Xs is standard translated Brownian motion. The expressions are similar to the Dyson-Phillips terms for magnetic Schrödinger semigroups.We use these expressions to establish properties of the solutions of certain Cauchy problems and we relate our results to the framework of generalised Dyson expansions as set up by Johnson and Lapidus.

scholarly journals Influence of strong time-dependent oscillations in semilinear damped wave models

2020 ◽  
Vol 17 (02) ◽  
pp. 395-442
Author(s):  
Halit Sevki Aslan ◽  
Michael Reissig
Keyword(s):  
Time Dependent ◽  
Small Data ◽  
Cauchy Problems ◽  
Damping Term ◽  
Wave Models ◽  
Time Existence

We study the global (in time) existence of small data solutions to some Cauchy problems for semilinear damped wave models with strong time-dependent oscillations. The goal is to understand the influence of strong oscillations in the coefficients on solutions to some semilinear models with an “effective-like” damping term, where the data are supposed to belong to different classes of regularity.

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