caa a22 4500 469108983 CHVBK 20180323133104.0 cr unu---uuuuu 170328e19920601xx s 000 0 eng 10.1007/BF00420586 doi (NATIONALLICENCE)springer-10.1007/BF00420586 Determination of source parameter in parabolic equations [Elektronische Daten] [J. Cannon, Yanping Lin, Shingmin Wang] 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. Kluwer Academic Publishers, 1992 Inverse problem nationallicence Parabolic equations nationallicence Cannon J. Department of Mathematics, Lamar University, 77710, Beaumont, Texas, USA aut Lin Yanping Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Canada aut Wang Shingmin Division of Mathematics and Computer Science, Northeast Missouri State University, 63501, Kirksville, MO, USA aut Meccanica Kluwer Academic Publishers 27/2(1992-06-01), 85-94 0025-6455 27:2<85 1992 27 11012 https://doi.org/10.1007/BF00420586 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00420586 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cannon J. Department of Mathematics, Lamar University, 77710, Beaumont, Texas, USA aut NATIONALLICENCE 700 1- Lin Yanping Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Canada aut NATIONALLICENCE 700 1- Wang Shingmin Division of Mathematics and Computer Science, Northeast Missouri State University, 63501, Kirksville, MO, USA aut NATIONALLICENCE 773 0- Meccanica Kluwer Academic Publishers 27/2(1992-06-01), 85-94 0025-6455 27:2<85 1992 27 11012 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer