Results 11 to 20 of about 1,036,048 (312)
Mild solutions for a class of fractional SPDEs and their sample paths [PDF]
Journal of Evolution Equations, 2009 In this article we introduce and analyze a notion of mild solution 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 infinite-dimensional fractional noise.
Pierre-A. Vuillermot, Marta Sanz-Solé
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Numerical analysis of nonlinear parabolic problems with variable exponent and $L^1$ data
Cubo, 2022 In this paper, we make the numerical analysis of the mild solution which is also an entropy solution of parabolic problem involving the $p(x)-$Laplacian operator with $L^1-$ data.
Stanislas Ouaro +2 more
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On the Positivity of Local Mild Solutions to Stochastic Evolution Equations [PDF]
, 2021 We provide sufficient conditions on the coefficients of a stochastic evolution equation on a Hilbert space of functions driven by a cylindrical Wiener process ensuring that its mild solution is positive if the initial datum is positive. As an application, we discuss the positivity of forward rates in the Heath-Jarrow-Morton model via Musiela's ...
Marinelli C., Scarpa L.
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A Semi-Linear Backward Parabolic cauchy Problem with Unbounded Coefficients of Hamilton-Jacobi-Bellman Type and Applications to optimal control [PDF]
, 2014 We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear ...
Addona, Davide
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Stability analysis of partial differential variational inequalities in Banach spaces
Nonlinear Analysis, 2020 In this paper, we study a class of partial differential variational inequalities. A general stability result for the partial differential variational inequality is provided in the case the perturbed parameters are involved in both the nonlinear mapping ...
Faming Guo +3 more
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Mathematics, 2023 This research delves into the field of fractional differential equations with both non-instantaneous impulses and delay within the framework of Banach spaces.
Abdellatif Benchaib +3 more
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On a class of stochastic partial differential equations [PDF]
, 2015 In this paper, we study the stochastic partial differential equation with multiplicative noise $\frac{\partial u}{\partial t} =\mathcal L u+u\dot W$, where $\mathcal L$ is the generator of a symmetric L\'evy process $X$ and $\dot W$ is a Gaussian noise ...
Song, Jian
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The Burgers equation driven by a stochastic measure
Modern Stochastics: Theory and Applications, 2023 The class of one-dimensional equations driven by a stochastic measure μ is studied. For μ only σ-additivity in probability is assumed. This class of equations includes the Burgers equation and the heat equation.
Vadym Radchenko
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Pathwise solutions and attractors for retarded SPDEs with time smooth diffusion coefficients [PDF]
, 2013 In this paper we study the longtime dynamics of mild solutions to retarded stochastic evolution systems driven by a Hilbert-valued Brownian motion. As a preparation for this purpose we have to show the existence and uniqueness of a cocycle solution of ...
Bessaih, Hakima +2 more
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Hölder estimates of mild solutions for nonlocal SPDEs [PDF]
Advances in Difference Equations, 2019 Abstract We consider nonlocal PDEs driven by additive white noises on Rd ${\mathbb{R}}^{d}$. For Lq $L^{q}$ integrable coefficients, we derive the existence and uniqueness, as well as Hölder continuity, of mild solutions.
Rongrong Tian +3 more
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