Results 51 to 60 of about 2,307 (91)
Well-posedness of the stochastic transport equation with unbounded drift
, 2017 The Cauchy problem for a multidimensional linear transport equation with unbounded drift is investigated. Provided the drift is Holder continuous , existence, uniqueness and strong stability of solutions are obtained.
Mollinedo, David A. C. +1 more
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Time--space white noise eliminates global solutions in reaction diffusion equations
, 2008 We prove that perturbing the reaction--diffusion equation $u_t=u_{xx} + (u_+)^p$ ($p>1$), with time--space white noise produces that solutions explodes with probability one for every initial datum, opposite to the deterministic model where a positive ...
Bandle +19 more
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On the Cauchy problem of a degenerate parabolic-hyperbolic PDE with Lévy noise
Advances in Nonlinear Analysis, 2017 In this article, we deal with the stochastic perturbation of degenerate parabolic partial differential equations (PDEs). The particular emphasis is on analyzing the effects of a multiplicative Lévy noise on such problems and on establishing a well ...
Biswas Imran H. +2 more
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A note on intermittency for the fractional heat equation [PDF]
, 2013 The goal of the present note is to study intermittency properties for the solution to the fractional heat equation $$\frac{\partial u}{\partial t}(t,x) = -(-\Delta)^{\beta/2} u(t,x) + u(t,x)\dot{W}(t,x), \quad t>0,x \in \bR^d$$ with initial condition ...
Balan, Raluca, Conus, Daniel
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A Differentiation Theory for It\^o's Calculus
, 2010 A peculiar feature of It\^o's calculus is that it is an integral calculus that gives no explicit derivative with a systematic differentiation theory counterpart, as in elementary calculus.
Bhattacharya R. +3 more
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Stochastic stability and instability of rumor model
Open MathematicsIn this study, we present a stochastic rumor model. The stability of the disease-free equilibrium state and instability of the free equilibrium E0{E}_{0} of stochastic epidemics model are considered with the help of Lyapunov functions.
Zhang Jing, Wang Xinyao, Wang Xiaohuan
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Absolute continuity for SPDEs with irregular fundamental solution
, 2014 For the class of stochastic partial differential equations studied in [Conus-Dalang,2008], we prove the existence of density of the probability law of the solution at a given point $(t,x)$, and that the density belongs to some Besov space.
Sanz-Solé, Marta, Süß, André
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Exponential mixing for some SPDEs with L\'evy noise
, 2010 We show how gradient estimates for transition semigroups can be used to establish exponential mixing for a class of Markov processes in infinite dimensions. We concentrate on semilinear systems driven by cylindrical $\alpha$-stable noises, $\alpha \in (0,
Priola, Enrico, Xu, Lihu, Zabczyk, Jerzy
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Decorrelation of total mass via energy [PDF]
, 2014 The main result of this small note is a quantified version of the assertion that if u and v solve two nonlinear stochastic heat equations, and if the mutual energy between the initial states of the two stochastic PDEs is small, then the total masses of ...
Chen, Le +2 more
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Early warning signs for SPDEs with continuous spectrum
European Journal of Applied MathematicsIn this work, we study early warning signs for stochastic partial differential equations (SPDEs), where the linearisation around a steady state is characterised by continuous spectrum. The studied warning sign takes the form of qualitative changes in the
Paolo Bernuzzi +2 more
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