The Cauchy problem for a linear parabolic partial differential equation |
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Authors: | Richard E Ewing |
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Institution: | Department of Mathematics, The Ohio State University, Columbus, Ohio 43210 USA |
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Abstract: | Numerical approximation of the solution of the Cauchy problem for the linear parabolic partial differential equation is considered. The problem: (p(x)ux)x ? q(x)u = p(x)ut, 0 < x < 1,0 < t? T; ; ; p(0) ux(0, t) = g(t), 0 < t0 ? t ? T, is ill-posed in the sense of Hadamard. Complex variable and Dirichlet series techniques are used to establish Hölder continuous dependence of the solution upon the data under the additional assumption of a known uniform bound for ¦ u(x, t)¦ when 0 ? x ? 1 and 0 ? t ? T. Numerical results are obtained for the problem where the data ?1, ?2 and g are known only approximately. |
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