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.

Read more about Heat Equation: Statement of The Equation, General Description, Solving The Heat Equation Using Fourier Series, Heat Conduction in Non-homogeneous Anisotropic Media, Fundamental Solutions, Mean-value Property For The Heat Equation, Stationary Heat Equation

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

... 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 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**...

**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)