Fritz John pp 461-465 | Cite as

Commentary on [39] and [47]

  • P. D. Lax
Part of the Contemporary Mathematicians book series (CM)


Paper [39] is concerned with the approximate solution of the backward heat equation:u t = u xx , x in R, - T < t ≤ 0. u(x, 0) f(x), under the assumption that u(x, t) ≥ 0. John shows that under this condition
$$\left| {f(x + iy)} \right| \leqslant {e^{{v^{2/4l}}}}\mu ,\mu = Maxf(x)$$
and | u(x, - a)| ≤ (1 - a T)-1 2 μ. John considers approximations ū to u of the following kind:
$$\bar u(x, - t) = \sum\limits_m^m {c_j^m} (t)\bar f(x + jh)$$
where h real and m an integer are parameters to be chosen, and f̄ is an approximation to f, obtained, e. g., by measurement. The measurement error is denoted by ɛ: ɛ = Max | f(x) - (x)|.


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© Springer Science+Business Media New York 1985

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  • P. D. Lax

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