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Diffusion subject to the specification of mass

1986; Elsevier BV; Volume: 115; Issue: 2 Linguagem: Inglês

10.1016/0022-247x(86)90012-0

1096-0813

John R. Cannon, John van der Hoek,

Advanced Mathematical Modeling in Engineering

Existence, uniqueness, and continuous dependence upon the data are demonstrated for the solution u = u(x, t) of the diffusion equation ut = uxx + s(x, t), 0 < x < 1, 0 < t ⩽ T, subject to u(x, 0) = ƒ(x), 0 < x < 1, ux(1, t) = g(t), 0 < t ⩽ T, and the specification of mass ∫0b(t) u(x, t) dx = m(t), 0 < b(t) < 1, 0 < t ⩽ T, where ∫0b(0) ƒ(x) dx = m(0). A numerical procedure is discussed and results of numerical experiments are presented.