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 ...
... 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 ...
... 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)