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Mild Solutions of Quantum Stochastic Differential Equations [PDF]
Electronic Communications in Probability, 2000 We introduce the concept of a mild solution for the right Hudson-Parthasarathy quantum stochastic differential equation, prove existence and uniqueness results, and show the correspondence between our definition and similar ideas in the theory of classical stochastic differential equations.
FAGNOLA, FRANCO, WILLS S. J.
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Mild Solution of Semilinear SPDEs with Young Drifts [PDF]
arXiv, 2023 In this paper, we study a semilinear SPDE with a linear Young drift $du_{t}=Lu_{t}dt+f\left(t, u_{t}\right)dt+\left(G_{t}u_{t}+g_{t}\right)d\eta_{t}+h\left(t, u_{t}\right)dW_{t}$, where $L$ is the generator of an analytical semigroup, $\eta$ is an $\alpha$-H\"older continuous path with $\alpha \in \left(1/2, 1\right)$ and $W$ is a Brownian motion ...
Liang, Jiahao, Tang, Shanjian
arxiv +3 more sources
On the equivalence of pathwise mild and weak solutions for quasilinear SPDEs [PDF]
arXiv, 2020 The main goal of this work is to relate weak and pathwise mild solutions for parabolic quasilinear stochastic partial differential equations (SPDEs). Extending in a suitable way techniques from the theory of nonautonomous semilinear SPDEs to the quasilinear case, we prove the equivalence of these two solution concepts.
Dhariwal, Gaurav +2 more
arxiv +6 more sources
Mild Solutions for Fractional Differential Equations with Nonlocal Conditions [PDF]
Advances in Difference Equations, 2010 This paper is concerned with the existence and uniqueness of mild solution of the fractional differential equations with nonlocal conditions , in a Banach space , where . General existence and uniqueness theorem, which extends many previous results, are given.
Fang Li
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On uniqueness of mild solutions for dissipative stochastic evolution equations [PDF]
arXiv, 2010 In the semigroup approach to stochastic evolution equations, the fundamental issue of uniqueness of mild solutions is often "reduced" to the much easier problem of proving uniqueness for strong solutions. This reduction is usually carried out in a formal way, without really justifying why and how one can do that.
Marinelli, Carlo, Röckner, Michael
arxiv +5 more sources
Remark on uniqueness of mild solutions to the Navier–Stokes equations
Journal of Functional Analysis, 2005 AbstractWe investigate a limiting uniqueness criterion to the Navier–Stokes equations. We prove that the mild solution is unique under the class C([0,T);bmo-1)∩Lloc∞((0,T);L∞), where bmo-1 is the “critical” space including Ln. As an application of uniqueness theorem, we also consider the local well-posedness of Navier–Stokes equations in bmo-1.
Hideyuki Miura
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AIMS Mathematics, 2022 This article contracts through Cauchy problems in infinite-dimensional Banach spaces towards a system of nonlinear non-autonomous mixed type integro-differential fractional evolution equation by nonlocal conditions through noncompactness measure (MNC ...
Naveed Iqbal +4 more
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Qualitative analysis of nonlinear implicit neutral differential equation of fractional order
AIMS Mathematics, 2021 In this paper, we discuss sufficient conditions for the existence of solutions for a class of Initial value problem for an neutral differential equation involving Caputo fractional derivatives. Also, we discuss some types of Ulam stability for this class
H. H. G. Hashem, Hessah O. Alrashidi
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Irregular convergence of mild solutions of semilinear equations [PDF]
Journal of Mathematical Analysis and Applications, 2019 We prove that even irregular convergence of semigroups of operators implies similar convergence of mild solutions of the related semi-linear equations with Lipschitz continuous nonlinearity. This result is then applied to three models originating from mathematical biology: shadow systems, diffusions on thin layers, and dynamics of ...
Adam Bobrowski, Markus Kunze
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AIMS Mathematics, 2020 This paper deals with the existence of mild solutions for non-linear fractional integrodifferential equations with state-dependent nonlocal conditions. The technique used is a generalization of the classical Darbo fixed point theorem for Fréchet spaces ...
Mouffak Benchohra +3 more
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