Heat Equation

The heat equation is a parabolic partial differential equation which describes the distribution of heat (or variation in temperature) in a given region over time.

Other articles related to "heat equation, equation, heat":

Lions–Lax–Milgram Theorem - Importance and Applications
... the power of Lions' theorem, consider the heat equation in n spatial dimensions (x) and one time dimension (t) where Δ denotes the Laplace operator ... arise immediately on what domain in spacetime is the heat equation to be solved, and what boundary conditions are to be imposed? The first question ... spatial region of interest, Ω, and a maximal time, T ∈(0, +∞], and proceeds to solve the heat equation on the "cylinder" One can then proceed to solve the heat equation using classical Lax ...
Fourier Series
... Fourier introduced the series for the purpose of solving the heat equation in a metal plate, publishing his initial results in his 1807 Mémoire sur la ... The heat equation is a partial differential equation ... Prior to Fourier's work, no solution to the heat equation was known in the general case, although particular solutions were known if the heat source behaved in a simple way, in particular, if ...
Heat Equation - Applications - Further Applications
... The heat equation arises in the modeling of a number of phenomena and is often used in financial mathematics in the modeling of options ... The famous Black–Scholes option pricing model's differential equation can be transformed into the heat equation allowing relatively easy solutions from a familiar ... The equation describing pressure diffusion in an porous medium is identical in form with the heat equation ...
Flow (mathematics) - Examples - Solutions of Heat Equation
... Let us consider the following Heat Equation on (for ) Equation corresponds to the Homogeneous Dirichlet boundary condition ... For any, we have With this operator, the heat equation becomes and ... Thus, the flow corresponding to this equation is (see notations above) ...

Famous quotes containing the words equation and/or heat:

A nation fights well in proportion to the amount of men and materials it has. And the other equation is that the individual soldier in that army is a more effective soldier the poorer his standard of living has been in the past.
Norman Mailer (b. 1923)

We’re having a heat wave, a tropical heat wave.
Irving Berlin (1888–1989)