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...al kind of [[Parabolic partial differential equation|parabolic]] [[partial differential equation]]s (PDEs) with a quadratic nonlinearity into a [[Heat equation|lin ...irst=Lawrence C. | authorlink=Lawrence C. Evans|title=Partial Differential Equations |publisher=American Mathematical Society |year=2010 |isbn= |edition=2nd |se ...

...mathematical study of [[Partial differential equation|partial differential equations]] (PDE) such as [[Laplace's equation]], about the [[integral#Terminology an ...ables as <math>x=(x_1,...,x_n)</math>. Representing the PDE as a partial [[differential operator]] <math>L</math> acting on an unknown function <math> ...

...d [[Parabolic partial differential equation|parabolic partial differential equations]]. ...ace=Berlin, Heidelberg|language=en|periodical=Abstract Parabolic Evolution Equations and Their Applications|series=Springer Monographs in Mathematics|title=Sect ...

...[[hyperbolic partial differential equation|hyperbolic partial differential equations]], it is unstable unless artificial viscosity is included. The abbreviation ...rder convergence in space. For example, in one dimension, if the [[partial differential equation]] is ...

.... |last2=Keyfitz |first2=N. |date=1997-09-01 |title=The McKendrick partial differential equation and its uses in epidemiology and population study |url=https://www ...ndent=:|equation=<math> \frac{\partial n}{\partial t} + \frac{\partial n}{\partial a} = - m(a)n </math>|border colour=#0073CF|background colour=#F5FFFA}}wher ...

...1928 in Osaka) is a retired Japanese mathematician who worked in [[partial differential equation]]s. He obtained his Ph.D. at the [[University of Tokyo]], under th ...-tokyo.ac.jp/record/39882/files/jfs130201.pdf }}</ref> studied the partial differential equation ...

...iginal equations, reducing the order of—all or some of—the highest-order [[partial derivative]]s. But the validity of the assumptions which are made need to b <math display="block">\nabla^2 E - \frac{1}{ c^2} \frac{\partial^2E}{\partial t^2} = 0\, ,</math> ...

== Parabolic model (non-relativistic) == ...ty Press |location=Oxford |year=1959 }}</ref> namely a [[parabolic partial differential equation]] of the kind: ...

{{short description|Framework for studying stochastic partial differential equations}} ...ardar–Parisi–Zhang equation]], the <math> \Phi_3^4</math> equation and the parabolic Anderson model, all of which require [[renormalization]] in order to have a ...

...ace operator''', is a quasilinear [[elliptic operator|elliptic]] [[partial differential operator]] of 2nd order. It is a nonlinear generalization of the [[Laplace :<math>\quad |\nabla u|^{p-2} = \left[ \textstyle \left(\frac{\partial u}{\partial x_1}\right)^2 ...

...rabolic partial differential equation|parabolic]], or [[hyperbolic partial differential equation|hyperbolic]]. The first well-documented ...tp://www.efunda.com/formulae/fluids/navier_stokes.cfm |title=Navier-Stokes Equations in Fluid Mechanics |publisher=Efunda.com |date= |accessdate=2013-10-29}}</r ...

...degree elements for any <math>2m</math>-th order of elliptic and parabolic equations in any spatial-dimension <math>\mathbb{R}^n</math> for <math>1\leq m \leq n d_{T,F,\beta}(v) = \frac{1}{|F|}\int_F \frac{\partial^{|\beta|v}}{\partial \nu_{F,1}^{\beta_1} \cdots \nu_{F,k}^{\beta_k}}. ...

...nal |title=A Class of Markov Processes Associated with Nonlinear Parabolic Equations |first=H. P. |last=McKean |author-link=Henry McKean |journal=[[Proceedings ...[Fokker-Planck equation]] for <math>\mu_t</math> is a non-linear [[partial differential equation]].<ref name=":1" /><ref name=":2" /> ...

...n to be expressed as one or more coupled first order ordinary differential equations. The following assumptions are generally made with CMT: ...base. The choice of the basis and the adoption of certain hypothesis like parabolic approximation differs from formulation to formulation. ...

...uation|wave]] equations) and all the others are put together, an ordinary "differential" equation with respect to the variable which was put in evidence is obtaine ...e equation<ref name="abstract">{{cite web |last1=Dezin |first1=A.A. |title=Differential equation, abstract |url=http://www.encyclopediaofmath.org/index.php?title=D ...

...frac{\partial T(x,t)}{\partial x}\right]=\lambda \frac{\partial^2 T(x,t)}{\partial x^2} + Q(x,t)</math> ...l t} = a \frac{\partial^2 T}{\partial x^2} - \epsilon u \frac{\partial T}{\partial x} + \frac{Q}{c \rho}</math> ...

{{Short description|Computational method for solving partial differential equations}} ...method used to solve [[Partial differential equation|partial differential equations]]. Its main advantage is it is very easy to understand and program on a com ...

* [[Partial differential equation]]s * [[Elliptic differential equation]]s ...

...as the [[integrator|time integrator]] for [[numerical partial differential equations]]. ...quations|hyperbolic]] as well as [[Parabolic partial differential equation|parabolic]] ...

{{Differential equations}} ...rds equation]] of underground water flow, the fully non-linear Leray—Lions equations.<ref>'''J. Leray and J. Lions.''' Quelques résultats de Višik sur les probl ...