Annali di Matematica Pura ed Applicata

, Volume 65, Issue 1, pp 377–387

# 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.

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