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Time-nonlocal evolution equations
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Toniazzi, Lorenzo (2018) Time-nonlocal evolution equations. PhD thesis, University of Warwick.
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WRAP_Theses_Toniazzi_2018.pdf - Submitted Version - Requires a PDF viewer. Download (1469Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3405229~S15
Abstract
Time-nonlocal evolution equations (EEs) are popular theoretical and applied models that introduce time-heterogeneity and memory effects in the classical heat equation. In this thesis we focus on wellposedness and Feynman-Kac formulae for several time-nonlocal EEs. In particular, we define and study a time-nonlocal initial condition, endowing it with probabilistic intuition. The main contribution is the stochastic-classical-wellposedness for the Marchaud EE and the stochastic-weak-wellposedness for the Marchaud-type EE. In the latter case, the kernel defining the nonlocal time derivative is allowed to be time-dependent. As a particular case we treat the Caputo-type inhomogeneous EE.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Evolution equations, Heat equation, Stochastic analysis | ||||
Official Date: | December 2018 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Kolokolʹt︠s︡ov, V. N. (Vasiliĭ Nikitich) | ||||
Sponsors: | Engineering and Physical Sciences Research Council | ||||
Format of File: | |||||
Extent: | 90 leaves : charts | ||||
Language: | eng |
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