The solution of the diffusion equation in two space variables subject to the specification of mass

Abstract

The Problem u_t = u_xx+u_yy, 0 < x,y < 1,0 < t ≤ T; u(x,y,0) = ƒ(x,y), 0 ≤ x,y ≤ 1; u (o,y,t) = g₀(y,t), u(1,y,t) = g₁(y,t), 0<y1,0<t≤T;u(x,1,t)=h₁(x,t), u(x,0,t)= μ(t)h₀(x), 0<x < 1,0 < t ≤ T; and , where ƒ g₀,g₁, h₀, h₁, s, and m are known functions while the function u and μ are unknown, is reduced to an equivalent integral equation for the unknown function μ(t). Existence and unicity are demonstrated. A numerical procedure is discussed along with some results of numerical experiments.

Keywords:

• Diffusion equation
• Integral boundary conditions

Additional information

Notes on contributors

John R. Cannon

John R. Cannon

Yanping Lin

Yanping Lin

Alec Matheson