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


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.


Error Analysis Heat Equation Space Variable Numerical Procedure Simple Formula 
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Copyright information

© Nicola Zanichelli Editore 1964

Authors and Affiliations

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

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