The optimal stability estimate for some ill-posed Cauchy problems for a parabolic equation
In: Mathematical Methods in the Applied Sciences, Jg. 10 (1988-11-01), S. 575-583
Online
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Zugriff:
In this paper we consider the non-characteristic Cauchy problem ut−a(x)uxx−b(x)ux−c(x)u = 0, x ∈ (0, l), t ∈ I, u(0, t) = φ(t), ux(0, t) = 0, t ∈ I, where I = ℝ or I = ℝ+ and u(x, 0) = 0, x ∈ [0, l], in the case I = ℝ+. Assuming an a priori bound for ‖u(l,.)‖, we derive the exact Holder type dependence of on ‖u(x,.)‖ on ‖φ‖.
| Titel: |
The optimal stability estimate for some ill-posed Cauchy problems for a parabolic equation
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| Autor/in / Beteiligte Person: | Vessella, Sergio ; Knabner, Peter |
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| Zeitschrift: | Mathematical Methods in the Applied Sciences, Jg. 10 (1988-11-01), S. 575-583 |
| Veröffentlichung: | Wiley, 1988 |
| Medientyp: | unknown |
| ISSN: | 1099-1476 (print) ; 0170-4214 (print) |
| DOI: | 10.1002/mma.1670100507 |
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