The heat equation

1. What is meant by heat equation?
2. How do you write a heat equation?
3. What is PDE heat equation?
4. What is the solution of heat equation?

What is meant by heat equation?

The heat equation (also known as the diffusion equation) describes a time-varying evolution of a function u(x, t) given its initial distribution u(x, 0). Physically, this PDE is used to determine the spatial distribution of temperature on a conductive surface after it diffuses for time t: (10)

How do you write a heat equation?

ut=a2uxx,0<x<L,t>0, where a is a positive constant determined by the thermal properties. This is the heat equation. u(x,0)=f(x),0≤x≤L.

What is PDE heat equation?

Here we consider the PDE ut = uxx, x ∈ (a, b),t> 0. (9) for u(x, t). This is the heat equation in the interval [a, b].

What is the solution of heat equation?

The heat equation is linear as u and its derivatives do not appear to any powers or in any functions. Thus the principle of superposition still applies for the heat equation (without side conditions). If u1 and u2 are solutions and c1,c2 are constants, then u=c1u1+c2u2 is also a solution.