Advertisement

Annali di Matematica Pura ed Applicata

, Volume 65, Issue 1, pp 377–387 | Cite as

A priori estimate for continuation of the solution of the heat equation in the space variable

  • J. R. Cannon
Article

Summary

Let u(x, t) satisfy the heat equation in a region D in the x−t plane and vanish initially. Let |u|<M0 in D and |u i 2 |<∈ in D* ⊂ D. Then, in D−D*, |u|<\(M_1 ^{1 - B_\varepsilon B} \), where B=B(x, t) satisfies O<B<1 and B(x, t) and M1 are given explicity by simple formulas. The a priori bound is applied to an error analysis of a numerical procedure for continuing solutions of the heat equation in the space variable.

Keywords

Error Analysis Heat Equation Space Variable Numerical Procedure Simple Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [1]
    J. R. Cannon,A Cauchy problem for the heat equation, to appear.Google Scholar
  2. [2]
    T. Carleman,Fonctions Quasi Analytiques, Paris, Ganthier-Villars, 1926, pp. 3–5.Google Scholar
  3. [3]
    R. Courant, andD. Hilbert,Methods of Mathematical Physics, Vol. II, Interscience Publishers (Wiley & Son), New York, 1962, p. 535.Google Scholar
  4. [4]
    Jim Douglas Jr.,Mathematical Programming and Integral Equations, Symposium, Provisional International Computation Centre, Birkhauser Verlag, Basel, 1960.Google Scholar
  5. [5]
    A. Friedman,Free boundary problems for parabolic equations I. Melting of Solids*, Journal of Mathematics and Mechanics, Vol. 8, N. 4 (1959).Google Scholar
  6. [6]
    Fritz John,Continuous dependence on the data for solutions of partial differential equaiions with a prescribed bound, Communications on Pure-and Applied Mathematics, Vol. XIII, pp. 551–585 (1960).Google Scholar

Copyright information

© Nicola Zanichelli Editore 1964

Authors and Affiliations

  • J. R. Cannon
    • 1
  1. 1.New YorkUSA

Personalised recommendations