Results 31 to 40 of about 1,036,048 (312)
Stability of mild solutions of the fractional nonlinear abstract Cauchy problem
Electronic Research Archive, 2022 Since the first work on Ulam-Hyers stabilities of differential equation solutions to date, many important and relevant papers have been published, both in the sense of integer order and fractional order differential equations.
J. Vanterler da C. Sousa +2 more
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Heat equation with general stochastic measure colored in time
Modern Stochastics: Theory and Applications, 2014 A stochastic heat equation on $[0,T]\times \mathbb{R}$ driven by a general stochastic measure $d\mu (t)$ is investigated in this paper. For the integrator μ, we assume the σ-additivity in probability only. The existence, uniqueness, and Hölder regularity
Vadym Radchenko
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Mild solutions of semilinear elliptic equations in Hilbert spaces
Journal of Differential Equations, 2017 This paper extends the theory of regular solutions ($C^1$ in a suitable sense) for a class of semilinear elliptic equations in Hilbert spaces. The notion of regularity is based on the concept of $G$-derivative, which is introduced and discussed. A result of existence and uniqueness of solutions is stated and proved under the assumption that the ...
Federico, Salvatore, Gozzi, Fausto
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On the equivalence of pathwise mild and weak solutions for quasilinear SPDEs
Stochastic Analysis and Applications, 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
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Existence and Uniqueness of Mild Solution for Fractional Integrodifferential Equations [PDF]
Advances in Difference Equations, 2010 We study the existence and uniqueness of mild solution of a class of nonlinear fractional integrodifferential equations dqu(t)/dtq+Au(t)=f(t,u(t))+∫0ta(t−s)g(s,u(s))ds, t∈[0,T], u(0)=u0, in a Banach space X, where 0<q<1. New results are obtained by fixed point theorem.
Fang Li, Gaston M. N’Guérékata
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Probabilistic representation for mild solution of the Navier–Stokes equations [PDF]
Mathematical Research Letters, 2021 This paper is based on a formulation of the Navier-Stokes equations developed by Iyer and Constantin \cite{Cont} , where the velocity field of a viscous incompressible fluid is written as the expected value of a stochastic process. Our contribution is to establish this probabilistic representation formula for mild solutions of the Navier-Stokes ...
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Estimates for mild solutions to semilinear Cauchy problems [PDF]
Electronic Journal of Differential Equations, 2014 The existence (and uniqueness) results on mild solutions of the abstract semilinear Cauchy problems in Banach spaces are well known. Following the results of Tartar (2008) and Burazin (2008) in the case of decoupled hyperbolic systems, we give an alternative proof, which enables us to derive an estimate on the mild solution and its time of existence ...
Burazin K., Erceg M.
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Viability result for semilinear functional differential inclusions in Banach spaces
Karpatsʹkì Matematičnì Publìkacìï, 2021 We show the existence result of a mild solution for a semilinear functional differential inclusion, with viability, governed by a family of linear operators. We consider the case when the constraint is moving.
M. Aitalioubrahim
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Intercrystalline cracking of mild steel in salt solutions [PDF]
Transactions of the Faraday Society, 1921 n ...
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Aronszajn-Hukuara type theorem for semilinear differential inclusions with nonlocal conditions [PDF]
, 2015 In this note we investigate the topological structure of the mild solution set of nonlocal Cauchy problems governed by semilinear differential inclusions in separable Banach spaces.
Cardinali, Tiziana, Rubbioni, Paola
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