Results 31 to 40 of about 1,033 (70)
Sub- and Super-solutions of a Nonlinear PDE, and Application to a Semilinear SPDE [PDF]
, 2013 2010 Mathematics Subject Classification: 35R60, 60H15, 74H35.We obtain upper and lower bounds for the explosion time of a semi-linear heat equation on a bounded $d$-dimensional domain, perturbed by white noise. The bounds we get are expressed in terms of
Kolkovska, E. T., López-Mimbela, J. A.
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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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On the Hausdorff dimension of regular points of inviscid Burgers equation with stable initial data
, 2007 Consider an inviscid Burgers equation whose initial data is a Levy a-stable process Z with a > 1. We show that when Z has positive jumps, the Hausdorff dimension of the set of Lagrangian regular points associated with the equation is strictly smaller ...
A.A. Novikov +17 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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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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Lifshits Tails for Squared Potentials
, 2018 We consider Schr\"odinger operators with a random potential which is the square of an alloy-type potential. We investigate their integrated density of states and prove Lifshits tails.
Kirsch, Werner, Raikov, Georgi
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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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Predictability of the Burgers dynamics under model uncertainty
, 2006 Complex systems may be subject to various uncertainties. A great effort has been concentrated on predicting the dynamics under uncertainty in initial conditions.
Blömker, Dirk, Duan, Jinqiao
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Invariant measures for monotone SPDE's with multiplicative noise term
, 2012 We study diffusion processes corresponding to infinite dimensional semilinear stochastic differential equations with local Lipschitz drift term and an arbitrary Lipschitz diffusion coefficient.
Es-Sarhir, A. +3 more
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Well-posedness of the non-local conservation law by stochastic perturbation
, 2019 Stochastic non-local conservation law equation in the presence of discontinuous flux functions is considered in an $L^{1}\cap L^{2}$ setting. The flux function is assumed bounded and integrable (spatial variable).
Olivera, Christian
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