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Title: Time-nonlocal evolution equations
Author: Toniazzi, Lorenzo
ISNI:       0000 0004 7972 4385
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2018
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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.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics