Results 101 to 110 of about 307,888 (268)
Electronic Journal of Differential Equations, 2013 In this article, we study a class of impulsive stochastic neutral partial functional differential equations in a real separable Hilbert space. By using Banach fixed point theorem, we give sufficient conditions for the existence and uniqueness of a ...
Danhua He, Liguang Xu
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Fractal and FractionalThis work investigates the solvability of the generalized Hilfer fractional inclusion associated with the solution set of a controlled system of minty type–fuzzy mixed quasi-hemivariational inequality (FMQHI).
Aeshah Abdullah Muhammad Al-Dosari
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2D Stochastic Chemotaxis-Navier-Stokes System [PDF]
arXiv, 2017 In this paper, we establish the existence and uniqueness of both mild(/variational) solutions and weak (in the sense of PDE) solutions of coupled system of 2D stochastic Chemotaxis-Navier-Stokes equations. The mild/variational solution is obtained through a fixed point argument in a purposely constructed Banach space.
arxiv
Existence and uniqueness of mild solution to fractional stochastic heat equation
Modern Stochastics: Theory and Applications, 2018 For a class of non-autonomous parabolic stochastic partial differential equations defined on a bounded open subset $D\subset {\mathbb{R}^{d}}$ and driven by an ${L^{2}}(D)$-valued fractional Brownian motion with the Hurst index $H>1/2$, a new result on ...
Kostiantyn Ralchenko, Georgiy Shevchenko
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Mild and viscosity solutions to semilinear parabolic path-dependent PDEs [PDF]
arXiv, 2016 We study and compare two concepts for weak solutions to semilinear parabolic path-dependent partial differential equations (PPDEs). The first is that of mild solutions as it appears, e.g., in the log-Laplace functionals of historical superprocesses. The aim of this paper is to show that mild solutions are also solutions in a viscosity sense.
arxiv
Particle dynamics subject to impenetrable boundaries: existence and uniqueness of mild solutions [PDF]
arXiv, 2018 We consider the dynamics of particle systems where the particles are confined by impenetrable barriers to a bounded, possibly non-convex domain $\Omega$. When particles hit the boundary, we consider an instant change in velocity, which turns the systems describing the particle dynamics into an ODE with discontinuous right-hand side.
arxiv
On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity [PDF]
arXiv, 2020 We investigate a stochastic partial differential equation with second order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by a space-time white noise. We introduce a notion of weak solution of this equation and prove its equivalence to the already known notion of mild solution.
arxiv
Учёные записки Казанского университета: Серия Физико-математические наукиFor a nonstrictly hyperbolic mildly quasilinear biwave equation in the first quadrant, an initial-boundary value problem with the Cauchy conditions specified on the spatial half-line and the Dirichlet and Wentzell conditions applied on the time half-line
V. I. Korzyuk, J. V. Rudzko
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Global Mild Solutions of the Navier-Stokes Equations
, 2012 Here we establish a global well-posedness of \textit{mild} solutions to the three-dimensional incompressible Navier-Stokes equations if the initial data are in the space $\mathcal{X}^{-1}$ defined by $(1.3)$ and if the norms of the initial data in $\mathcal{X}^{-1}$ are bounded exactly by the viscosity coefficient $ $.
Lei, Zhen, Lin, Fang-hua
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Electronic Journal of Qualitative Theory of Differential Equations, 2012 In this work, we prove a result on the local existence of mild solution in the $\alpha$-norm for some partial functional differential equations with infinite delay. We suppose that the linear part generates a compact analytic semigroup.
Khalil Ezzinbi, Amor Rebey
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