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  • ...ation for which the opposite happens. In order to check whether a nonlocal equations holds at a point, information about the values of the function far from tha ...ng the [[fractional Laplacian]] are the prime example of nonlocal elliptic equations. ...
    4 KB (619 words) - 13:34, 5 May 2014
  • ...s to a variety of methods to prove existence, uniqueness or regularity for equations that are in some sense ''close'' to an equation that is well understood. If # Well posedness results for evolution equations locally in time. ...
    2 KB (351 words) - 13:17, 4 March 2014
  • ...uation of order $\sigma$ is the name currently given to two very different equations, namely ...xtremely different behaviors. They are both fractional order [[Quasilinear equations]]. ...
    3 KB (387 words) - 21:48, 15 April 2015
  • <div style="top:+0.2em; font-size:95%;">This is the Nonlocal Equations Wiki</div> ...find information on a specific topic, you may want to check the [[list of equations]] or use the search option on the left. ...
    4 KB (596 words) - 14:09, 23 September 2013
  • * The [[Boltzmann equation]] models the evolution of dilute gases and it is intrinsically an integral equation. In fact, simp ...tic models, in particular particle systems, can be used to derive nonlocal equations like the [[Nonlocal porous medium equation]], the [[Hamilton-Jacobi equatio ...
    2 KB (291 words) - 11:31, 17 November 2012
  • The surface quasi-geostrophic (SQG) equation consists of an evolution equation for a scalar function $\theta: \R^+ \times \R^2 \to \R$. In the in * '''Evolution of a modulus of continuity''' <ref name="KNV"/>: An explicit modulus of con ...
    9 KB (1,363 words) - 14:47, 8 May 2012
  • * Improve the page on [[Active scalar equations]]. ...Nonlocal Phase Field Equations]] this will include many types of evolution equations such as nonlocal reaction-diffusion, models arising from nonlocal ising mod ...
    4 KB (582 words) - 16:11, 25 January 2016
  • ...icles in a gas, but only statistically. However, this equation and related equations are used in other physical situations, such as in optics. The corresponding ...t a single equation but a family of equations, where one obtains different equations depending on the nature of the interaction between particles (see below). A ...
    8 KB (1,331 words) - 11:07, 30 August 2016
  • ...between two nearby horizontal plates<ref name="MR0097227"/>. The following equations are given for a non-negative pressure $u=u(x,t)$, supported in in a time de ...
    3 KB (481 words) - 07:45, 1 August 2016
  • ...linear term plus a lower order nonlinear term. For elliptic and parabolic equations, the two effective possibilities for the linear term is to be either the [[ ...he definition above are still considered semilinear. For example evolution equations of the form ...
    8 KB (1,177 words) - 14:27, 15 May 2015
  • A drift-(fractional)diffusion equation refers to an evolution equation of the form ...equations from fluid dynamics (for example the [[surface quasi-geostrophic equations]]). For this reason, the assumption that $\mathrm{div} \ b = 0$ is taken so ...
    8 KB (1,222 words) - 10:22, 14 April 2015
  • result. The corresponding result for elliptic equations of second order is the ...nack inequality. However, there are simple example of integro-differential equations for which the Hölder estimates hold and the Harnack inequality does not <r ...
    18 KB (2,683 words) - 10:40, 8 July 2016