Results 21 to 30 of about 963 (56)

Linear-implicit strong schemes for Itô-Galkerin approximations of stochastic PDEs [PDF]

, 2010
Linear-implicit versions of strong Taylor numerical schemes for finite dimensional Itô stochastic differential equations (SDEs) are shown to have the same order as the original scheme.
Kloeden, Peter E., Shott, Stephen
core  

An invariant in shock clustering and Burgers turbulence

, 2012
1-D scalar conservation laws with convex flux and Markov initial data are now known to yield a completely integrable Hamiltonian system. In this article, we rederive the analogue of Loitsiansky's invariant in hydrodynamic turbulence from the perspective ...
Burgers J M, Burgers J M, Burgers J M, Burgers J M, Burgers J M, Carraro L, Kolmogorov A N, Loitsianskii L G, Menon G, Ravi Srinivasan, Woyczyński W A   +10 more
core   +1 more source

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., Olivera, Christian   +1 more
core   +1 more source

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
core   +1 more source

Early warning signs for SPDEs with continuous spectrum

European Journal of Applied Mathematics
In 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, Antonia Freya Susanne Düx, Christian Kuehn   +2 more
doaj   +1 more source

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, Buckdahn, Budd, Cortázar, Dávila, Ferreira, Ferreira, Galaktionov, Groisman, Gyöngy, Gyöngy, Julian Fernández Bonder, Karatzas, Mao, Mueller, Mueller, Mueller, Pablo Groisman, Samarskii, Walsh   +19 more
core   +1 more source

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, A.W. Janicki, G. Molchan, G. Samorodnitsky, J. Bertoin, J. Bertoin, K. Handa, L. Carraro, L. Chaumont, L. Chaumont, L. Marsalle, M. Goldman, N.H. Bingham, R. Holley, T. Simon, Thomas Simon, W.A. Woyczynski, Ya.G. Sinai   +17 more
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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, Khoshnevisan, Davar, Kim, Kunwoo   +2 more
core  

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
core   +2 more sources