Zobrazeno 1 - 10
of 104
pro vyhledávání: '"60H17"'
The Stochastic Burgers Equation (SBE) is a singular, non-linear Stochastic Partial Differential Equation (SPDE) that describes, on mesoscopic scales, the fluctuations of stochastic driven diffusive systems with a conserved scalar quantity. In space d
Externí odkaz:
http://arxiv.org/abs/2501.00344
Autor:
Sauer, Jonas, Smith, Scott A.
In this expository note, we show that the blow-up arguments of L. Simon adapt well to the corresponding Schauder theory of germs used in the study of singular SPDEs. We illustrate this through some representative examples. As in the classical PDE fra
Externí odkaz:
http://arxiv.org/abs/2412.01486
Autor:
Sritharan, Sivaguru S., Mudaliar, Saba
In this paper we study a large class of nonlinear stochastic wave equations that arise in laser generation models and models for propagation in random media in a unified mathematical framework. Continuous and pulse-wave propagation models, free elect
Externí odkaz:
http://arxiv.org/abs/2411.16013
Autor:
Schiavo, Lorenzo Dello
We develop a unifying theory for four different objects: (1) infinite systems of interacting massive particles; (2) solutions to the Dean-Kawasaki equation with singular drift and space-time white noise; (3) Wasserstein diffusions with a.s. purely at
Externí odkaz:
http://arxiv.org/abs/2411.14936
In this paper we extend the theory of energy solutions for singular SPDEs, focusing on equations driven by highly irregular noise with bilinear nonlinearities, including scaling critical examples. By introducing Gelfand triples and leveraging infinit
Externí odkaz:
http://arxiv.org/abs/2411.07680
Autor:
Goldys, Ben, Peszat, Szymon
Let $P_s\phi(x)=\mathbb{E}\, \phi(X^x(s))$, be the transition semigroup on the space $B_b(E)$ of bounded measurable functions on a Banach space $E$, of the Markov family defined by the linear equation with additive noise $$ d X(s)= \left(AX(s) + a\ri
Externí odkaz:
http://arxiv.org/abs/2410.20074
Autor:
Martini, Adrian, Mayorcas, Avi
We study an additive-noise approximation to Keller--Segel--Dean--Kawasaki dynamics which is proposed as an approximate model to the fluctuating hydrodynamics of chemotactically interacting particles around their mean-field limit. Two parameters play
Externí odkaz:
http://arxiv.org/abs/2410.17022
Autor:
Bringmann, Bjoern, Cao, Sky
We prove the global well-posedness of the dynamical sine-Gordon model up to the third threshold, i.e., for parameters $\beta^2 < 6\pi$. The key novelty in our approach is the introduction of the so-called resonant equation, whose solution is entirely
Externí odkaz:
http://arxiv.org/abs/2410.15493
Consider the stochastic heat equation \begin{equation*} \partial_t u_t(x)=\frac12 \partial^2_{xx}u_t(x) +b(u_t(x))+\dot{W}_{t}(x),\quad t\in(0,T],\, x\in D, \end{equation*} where $b$ is a generalized function, $D$ is either $[0,1]$ or $\mathbb{R}$, a
Externí odkaz:
http://arxiv.org/abs/2410.06599
Autor:
Yang, Kevin
We derive the KPZ equation as a continuum limit of height functions in asymmetric simple exclusion processes with drift that depends on the local particle configuration. To our knowledge, it is a first such result for a class of particle systems with
Externí odkaz:
http://arxiv.org/abs/2409.10513