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

1993; Taylor & Francis; Volume: 50; Issue: 1-2 Linguagem: Inglês

10.1080/00036819308840181

1563-504X

John R. Cannon, John R. Cannon, Yanping Lin, Yanping Lin, Alec Matheson, Alec Matheson,

Numerical methods in inverse problems

Abstract The Problem ut = uxx+uyy, 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 equationIntegral boundary conditions Additional informationNotes on contributorsJohn R. Cannon John R. Cannon Yanping Lin Yanping Lin Alec Matheson