Results 1 to 10 of about 4,498 (109)

Renormalisation of parabolic stochastic PDEs [PDF]

, 2018
We give a survey of recent result regarding scaling limits of systems from statistical mechanics, as well as the universality of the behaviour of such systems in so-called cross-over regimes.
Hairer, Martin
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Condensation phenomena in nonlinear drift equations [PDF]

, 2013
We study nonnegative, measure-valued solutions to nonlinear drift type equations modelling concentration phenomena related to Bose-Einstein particles. In one spatial dimension, we prove existence and uniqueness for measure solutions.
Carrillo, Jose' A., Di Francesco, Marco, Toscani, Giuseppe   +2 more
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Vanishing viscosity limits of mixed hyperbolic–elliptic systems arising in multilayer channel flows [PDF]

, 2015
This study considers the spatially periodic initial value problem of 2 × 2 quasilinear parabolic systems in one space dimension having quadratic polynomial flux functions.
Papaefthymiou, ES, Papageorgiou, DT
core   +1 more source

Fine properties of functions of bounded deformation - an approach via linear PDES [PDF]

, 2020
In this survey we collect some recent results obtained by the authors and collaborators concerning the fine structure of functions of bounded deformation (BD).
De Philippis, Guido, Rindler, Filip
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Rigorous Numerical Verification of Uniqueness and Smoothness in a Surface Growth Model [PDF]

, 2015
Based on numerical data and a-posteriori analysis we verify rigorously the uniqueness and smoothness of global solutions to a scalar surface growth model with striking similarities to the 3D Navier--Stokes equations, for certain initial data for which ...
Blömker, Dirk, Nolde, Christian, Robinson, James C.   +2 more
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A study of blow-ups in the Keller-Segel model of chemotaxis [PDF]

, 2010
We study the Keller-Segel model of chemotaxis and develop a composite particle-grid numerical method with adaptive time stepping which allows us to accurately resolve singular solutions.
Bertozzi A, Biler P Corrias L Dolbeault J, Blanchet A, Chayes L Panferov V, Havlac K, Hortsmann D, Hortsmann D, Ibrahim Fatkullin, Karlin S, McKean H P, Patlak C S, Sire C Chavanis P-H, Strehl R, Strehl R Sokolov A Kuzmin D Hortsmann D Turek S, Sznitman A, Villani C   +15 more
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A moving mesh method with variable relaxation time

, 2006
We propose a moving mesh adaptive approach for solving time-dependent partial differential equations. The motion of spatial grid points is governed by a moving mesh PDE (MMPDE) in which a mesh relaxation time \tau is employed as a regularization ...
Adjerid, Ali Reza Soheili, Ascher, Baines, Bebernes, Budd, Budd, Carlson, Coyle, Friedman, Huang, Huang, Hyman, John M. Stockie, Li, Lipnikov, Petzold, Sanz-Serna, Stockie, Tan, Tang   +20 more
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The Burgers' equation with stochastic transport: shock formation, local and global existence of smooth solutions

, 2019
In this work, we examine the solution properties of the Burgers' equation with stochastic transport. First, we prove results on the formation of shocks in the stochastic equation and then obtain a stochastic Rankine-Hugoniot condition that the shocks ...
Alonso-Orán, Diego, de León, Aythami Bethencourt, Takao, So   +2 more
core   +1 more source

Algebraic varieties in Birkhoff strata of the Grassmannian Gr$\mathrm{^{(2)}}$: Harrison cohomology and integrable systems

, 2011
Local properties of families of algebraic subsets $W_g$ in Birkhoff strata $\Sigma_{2g}$ of Gr$^{(2)}$ containing hyperelliptic curves of genus $g$ are studied.
Ablowitz M J, Agafonov S I, Arnold V I, B G Konopelchenko, Benney D Y, Casian L Kodama Y, Dubrovin B A, Dubrovin B A, Dubrovin B A, Dubrovin B A, Dubrovin B A, Dubrovin B A, Frönsdal C, G Ortenzi, Harris J, Kodama Y, Konopelchenko B G, Konopelchenko B G, Konopelchenko B G, Konopelchenko B G Ortenzi G, Krichever I M, Krichever I M, Krichever I M, Krichever I M, Lax P D, Lichtenbann S, Mulase M, Mulase M, Nakayashiki A, Presley A, Shafarevich I R, Silverman J, Whitham G B, Whitham G B, Zakharov V E, Zakharov V E, Zakharov V E   +36 more
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The strong Feller property for singular stochastic PDEs [PDF]

, 2016
We show that the Markov semigroups generated by a large class of singular stochastic PDEs satisfy the strong Feller property. These include for example the KPZ equation and the dynamical $\Phi^4_3$ model. As a corollary, we prove that the Brownian bridge
Hairer, M, Mattingly, J
core   +3 more sources