Determination of source parameter in parabolic equations |
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Authors: | J R Cannon Yanping Lin Shingmin Wang |
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Institution: | (1) Department of Mathematics, Lamar University, 77710 Beaumont, Texas, USA;(2) Department of Mathematics, University of Alberta, T6G 2G1 Edmonton, Canada;(3) Division of Mathematics and Computer Science, Northeast Missouri State University, 63501 Kirksville, MO, USA |
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Abstract: | The authors consider the problem of finding u=u(x, t) and p=p(t) which satisfy u = Lu + p(t) + F(x, t, u, x, p(t)) in Q T=Ω×(0, T], u(x, 0)=ø(x), x∈Ω, u(x, t)=g(x, t) on ?Ω×(0, T] and either ∫G(t) Φ(x,t)u(x,t)dx = E(t), 0 ? t ? T or u(x0, t)=E(t), 0≤t≤T, where Ω?R n is a bounded domain with smooth boundary ?Ω, x 0∈Ω, L is a linear elliptic operator, G(t)?Ω, and F, ø, g, and E are known functions. For each of the two problems stated above, we demonstrate the existence, unicity and continuous dependence upon the data. Some considerations on the numerical solution for these two inverse problems are presented with examples. |
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Keywords: | Inverse problem Parabolic equations |
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