OPTIMAL CONTROL PROBLEMS CONSTRAINED BY FRACTIONAL PDES AND APPLICATION TO DEEP NEURAL NETWORKS [PDF]
, 2021 Motivated by several applications in geophysics, imaging, machine learning, elasticity, finance, anomalous diffusion, etc., this thesis develops algorithms to solve optimal control problems constrained by fractional partial differential equations (FPDEs).
Deepanshu Verma
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Path regularity and explicit convergence rate for BSDE with truncated quadratic growth [PDF]
, 2010 We consider backward stochastic differential equations with drivers of quadratic growth (qgBSDE). We prove several statements concerning path regularity and stochastic smoothness of the Solution processes of the qg-BSDE, in particular we prove an ...
Dos Reis, Goncalo, Imkeller, Peter
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Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity [PDF]
, 2016 We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of ...
Haji-Ali, Abdul-Lateef +8 more
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Besov regularity of elliptic and parabolic PDEs with inhomogeneous boundary conditions on Lipschitz domains [PDF]
, 2022 This dissertation connects different topics and shows new results in the research field of applied analysis. We investigate the regularity of solutions of partial differential equations (=PDEs) of elliptic and parabolic type on non-smooth domains ...
Szemenyei, Flóra Orsolya
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WELL-POSEDNESS FOR SOME NON-LINEAR DIFFUSION PROCESSES AND RELATED PDE ON THE WASSERSTEIN SPACE [PDF]
, 2022 International audienceIn this paper, we investigate the well-posedness of the martingale problem associated to non-linear stochastic differential equations (SDEs) in the sense of McKean-Vlasov under mild assumptions on the coefficients as well as ...
Frikha, Noufel +1 more
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Local existence, uniqueness, and smooth dependence for nonsmooth quasilinear parabolic problems [PDF]
, 2009 A general theory on local existence, uniqueness, regularity, and smooth dependence in H"older spaces for a general class of quasilinear parabolic initial boundary value problems with nonsmooth data has been developed.
Jens André Griepentrog +3 more
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Regularity problem for quasilinear elliptic and parabolic systems [PDF]
, 1995 The smoothness of solutions for quasilinear systems is one of the most important problems in modern mathematical physics. This book deals with regular or strong solutions for general quasilinear second-order elliptic and parabolic systems.
Koshelev, Alexander
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Approximation of random/stochastic partial differential equations [PDF]
, 2018 The overarching interest of this thesis lies in approximations of partial differential equations (PDEs) with randomness or stochasticity. We focus on three rather different problems: a study of random fields on spherical shells, and its applications to ...
Kazashi, Yoshihito
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A numerical framework for solving PDE-constrained optimization problems from multiscale particle dynamics [PDF]
, 2023 In this thesis, we develop accurate and efficient numerical methods for solving partial differential equation (PDE) constrained optimization problems arising from multiscale particle dynamics, with the aim of producing a desired time-dependent state at ...
Aduamoah, Mildred
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Spatial smoothness of the stationary solutions of the 3D Navier--Stokes equations [PDF]
, 2006 International audienceWe consider stationary solutions of the three dimensional Navier--Stokes equations (NS3D) with periodic boundary conditions and driven by an external force which might have a deterministic and a random part.
Odasso, Cyril
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