Global existence and stability for an inverse coefficient problem for a semilinear parabolic equation

被引：0

作者：

Mourad Choulli

Masahiro Yamamoto

机构：

[1] LMAM,Graduate School of Mathematical Sciences

[2] UMR 7122,undefined

[3] Université Paul Verlaine-Metz et CNRS,undefined

[4] University of Tokyo,undefined

来源：

Archiv der Mathematik | 2011年 / 97卷

关键词：

35R30; Laser material treatments; Global existence; Uniqueness; Stability; Inverse coefficient problem; Semilinear parabolic equation; Integral equation;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We establish the global existence, the uniqueness and the stability for an inverse coefficient problem for a semilinear parabolic equation. This problem is motivated by an application related to laser material treatments, and our result is a continuation of the previous work by Hömberg and Yamamoto (Inverse Problems 22:1855–1867, 2006). We transform our inverse problem into a nonlinear integral equation of second kind, which is solved locally by the contraction mapping principle. Next we prove that the maximal solution of the integral equation is a global solution.

引用

页码：587 / 597

页数：10

共 5 条

[1]

Hömberg D.(2006)On an inverse problem related to laser material treatments Inverse Problems 22 1855-1867

[2]

Yamamoto M(1985)On the abstract Cauchy problem of parabolic type in spaces of continuous functions J. Math. Anal. Appl. 107 16-66

[3]

Sinestrari E.(1974)Generation of analytic semigroups by strongly elliptic operators Trans. Amer. Math. Soc. 199 141-162

[4]

Stewart H.B.(1980)Generation of analytic semigroups by strongly elliptic operators under general boundary conditions Trans. Amer. Math. Soc. 259 299-310

[5]

Stewart H.B.(undefined)undefined undefined undefined undefined-undefined

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