# Category: Parabolic partial differential equations

Turing pattern
The Turing pattern is a concept introduced by English mathematician Alan Turing in a 1952 paper titled "The Chemical Basis of Morphogenesis" which describes how patterns in nature, such as stripes and
Von Foerster equation
The McKendrick–von Foerster equation is a linear first-order partial differential equation encountered in several areas of mathematical biology – for example, demography and cell proliferation modelin
Feynman–Kac formula
The Feynman–Kac formula, named after Richard Feynman and Mark Kac, establishes a link between parabolic partial differential equations (PDEs) and stochastic processes. In 1947, when Kac and Feynman we
Reaction–diffusion system
Reaction–diffusion systems are mathematical models which correspond to several physical phenomena. The most common is the change in space and time of the concentration of one or more chemical substanc
Fokker–Planck equation
In statistical mechanics, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of the velocity of a particle under the in
The Chemical Basis of Morphogenesis
"The Chemical Basis of Morphogenesis" is an article that the English mathematician Alan Turing wrote in 1952. It describes how patterns in nature, such as stripes and spirals, can arise naturally from
Parabolic partial differential equation
A parabolic partial differential equation is a type of partial differential equation (PDE). Parabolic PDEs are used to describe a wide variety of time-dependent phenomena, including heat conduction, p
Diffusion equation
The diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements a
Mehler kernel
The Mehler kernel is a complex-valued function found to be the propagator of the quantum harmonic oscillator.
Heat equation
In mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions. The theory of the heat equation was f
Autowave
Autowaves are self-supporting non-linear waves in active media (i.e. those that provide distributed energy sources). The term is generally used in processes where the waves carry relatively low energy
Autowave reverberator
In the theory of autowave phenomena an autowave reverberator is an autowave vortex in a two-dimensional active medium. A reverberator appears a result of a rupture in the front of a plane autowave. Su
Kolmogorov backward equations (diffusion)
The Kolmogorov backward equation (KBE) (diffusion) and its adjoint sometimes known as the Kolmogorov forward equation (diffusion) are partial differential equations (PDE) that arise in the theory of c
Convection–diffusion equation
The convection–diffusion equation is a combination of the diffusion and convection (advection) equations, and describes physical phenomena where particles, energy, or other physical quantities are tra
Heat kernel
In the mathematical study of heat conduction and diffusion, a heat kernel is the fundamental solution to the heat equation on a specified domain with appropriate boundary conditions. It is also one of
Numerical solution of the convection–diffusion equation
The convection–diffusion equation describes the flow of heat, particles, or other physical quantities in situations where there is both diffusion and convection or advection. For information about the