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":

... 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 propagation de la chaleur dans les corps ... 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 ...

**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 body of mathematics ... The

**equation**describing pressure diffusion in an porous medium is identical in form with the

**heat equation**...

... To illustrate the power of Lions' theorem, consider the

**heat equation**in n spatial dimensions (x) and one time dimension (t) where Δ denotes the ... Two questions 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 — the shape of the domain — is the one in which ... 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 ...

**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:

“Jail sentences have many functions, but one is surely to send a message about what our society abhors and what it values. This week, the *equation* was twofold: female infidelity twice as bad as male abuse, the life of a woman half as valuable as that of a man. The killing of the woman taken in adultery has a long history and survives today in many cultures. One of those is our own.”

—Anna Quindlen (b. 1952)

“And suddenly, to be dying

Is not a little or mean or cheap thing,

Only wearying, the *heat* unbearable ...”

—John Ashbery (b. 1927)