Searched for: subject%3A%22evolution%255C+equations%22
(1 - 19 of 19)
document
Agresti, A. (author), Veraar, M.C. (author)
In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi- or semi-linear type. Our results improve many of the abstract results in the classical variational setting. In particular, we are able to replace the usual weak or local monotonicity condition by a more flexible local Lipschitz...
journal article 2024
document
Böhm, Udo (author)
The stochastic FitzHugh-Nagumo equations are a system of stochastic partial differential equations that describes the propagation of action potentials along nerve axons. In the present work we obtain well-posedness and regularisation results for the FitzHugh-Nagumo equations with domain R^d. We begin by considering the weak critical variational...
master thesis 2023
document
Agresti, Antonio (author), Veraar, M.C. (author)
This paper is a continuation of Part I of this project, where we developed a new local well-posedness theory for nonlinear stochastic PDEs with Gaussian noise. In the current Part II we consider blow-up criteria and regularization phenomena. As in Part I we can allow nonlinearities with polynomial growth and rough initial values from critical...
journal article 2022
document
Agresti, Antonio (author), Veraar, M.C. (author)
In this paper we develop a new approach to nonlinear stochastic partial differential equations with Gaussian noise. Our aim is to provide an abstract framework which is applicable to a large class of SPDEs and includes many important cases of nonlinear parabolic problems which are of quasi- or semilinear type. This first part is on local...
journal article 2022
document
van Neerven, J.M.A.M. (author), Veraar, M.C. (author)
This paper presents a survey of maximal inequalities for stochastic convolutions in 2-smooth Banach spaces and their applications to stochastic evolution equations. This article is part of the theme issue 'Semigroup applications everywhere'.
review 2020
document
Lü, Qi (author), van Neerven, J.M.A.M. (author)
Extending results of Pardoux–Peng and Hu–Peng, we prove well-posedness results for backward stochastic evolution equations in UMD Banach spaces.
book chapter 2019
document
Bruell, G. (author), Ehrnström, Mats (author), Geyer, A. (author), Pei, Long (author)
We show that for a large class of evolutionary nonlinear and nonlocal partial differential equations, symmetry of solutions implies very restrictive properties of the solutions and symmetry axes. These restrictions are formulated in terms of three principles, based on the structure of the equations. The first principle covers equations that...
journal article 2017
document
Veraar, M.C. (author), Yaroslavtsev, I.S. (author)
In this paper we define a new type of quadratic variation for cylindrical continuous local martingales on an infinite dimensional spaces. It is shown that a large class of cylindrical continuous local martingales has such a quadratic variation. For this new class of cylindrical continuous local martingales we develop a stochastic integration...
journal article 2016
document
Gallarati, C. (author), Veraar, M.C. (author)
In this paper we study maximal Lp-regularity for evolution equations with time-dependent operators A. We merely assume a measurable dependence on time. In the first part of the paper we present a new sufficient condition for the Lp-boundedness of a class of vector-valued singular integrals which does not rely on Hörmander conditions in the time...
journal article 2016
document
Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author)
In this paper, we prove maximal regularity estimates in “square function spaces” which are commonly used in harmonic analysis, spectral theory, and stochastic analysis. In particular, they lead to a new class of maximal regularity results for both deterministic and stochastic equations in L p -spaces with 1<p<?. For stochastic equations, the...
journal article 2015
document
Pronk, M. (author)
In this thesis we study stochastic evolution equations in Banach spaces. We restrict ourselves to the two following cases. First, we consider equations in which the drift is a closed linear operator that depends on time and is random. Such equations occur as mathematical models in for instance mathematical finance and filtration theory. Second,...
doctoral thesis 2013
document
Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author)
journal article 2012
document
Cox, S.G. (author), Van Neerven, J.M.A.M. (author)
journal article 2010
document
Van Neerven, J.M.A.M. (author), Weis, L. (author)
journal article 2008
document
Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author)
journal article 2008
document
Brzezniak, Z. (author), Van Neerven, J.M.A.M. (author), Veraar, M.C. (author), Weis, L. (author)
Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Itô formula is proved which is applied to prove the existence of strong solutions for a class of stochastic evolution equations in UMD Banach spaces. The abstract results are applied to prove regularity in space and...
journal article 2008
document
Veraar, M.C. (author)
Stochastic partial differential equations (SPDEs) of evolution type are usually modelled as ordinary stochastic differential equations (SDEs) in an infinite-dimensional state space. In many examples such as the stochastic heat and wave equation, this viewpoint may lead to existence and uniqueness results and regularity properties. To model the...
doctoral thesis 2006
document
Van Gaans, O. (author), Van Neerven, J. (author)
We investigate existence and permanence properties of invariant measures for abstract stochastic Cauchy problems of the form
journal article 2006
document
Van Neerven, J.M.A.M. (author), Weis, L. (author)
journal article 2006
Searched for: subject%3A%22evolution%255C+equations%22
(1 - 19 of 19)