Choulli, M.; Yamamoto, M. Conditional stability in determining a heat source. (English) Zbl 1081.35136 J. Inverse Ill-Posed Probl. 12, No. 3, 233-243 (2004). Summary: We establish the uniqueness and conditional stability in determining a heat source term from boundary measurements which are started after some time. The key is analyticity of solutions in the time and we apply the maximum principle for analytic functions. Cited in 49 Documents MSC: 35R30 Inverse problems for PDEs 35K05 Heat equation 35B50 Maximum principles in context of PDEs Keywords:uniqueness; conditional stability; heat source; boundary measurements PDFBibTeX XMLCite \textit{M. Choulli} and \textit{M. Yamamoto}, J. Inverse Ill-Posed Probl. 12, No. 3, 233--243 (2004; Zbl 1081.35136) Full Text: DOI References: [1] R. A. Adams, Sobolev Spaces. Academic Press, New York, 1975. [2] DOI: 10.1137/0705024 · Zbl 0176.15403 · doi:10.1137/0705024 [3] J. R. Cannon, The One-dimensional Heat Equation. Addison-Wesley Publishing Company, Reading, 1984. · Zbl 0567.35001 [4] Proc. Japan Acad. 43 pp 82– (1967) [5] Hayden F. J., Pacific J. Math. 57 pp 423– (1975) [6] M. M. Lavrentiev, V. G. Romanov, and V. G. Vasiliev, Multidimensional Inverse Problems for Differential Equations. Lecture Notes in Mathematics, Vol. 167. Springer-Verlag, Berlin, 1970. · Zbl 0208.36403 [7] J. L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications. English translation. Springer-Verlag, Berlin, 1972. · Zbl 0223.35039 [8] Univ. of Kyoto, Series A 31 pp 219– (1958) [9] S. Mizohata, The Theory of Partial Differential Equations. Cambridge University Press, London, 1973. · Zbl 0263.35001 [10] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, Berlin, 1983. · Zbl 0516.47023 [11] H. Tanabe, Equations of Evolution. Pitman, London, 1979. · Zbl 0417.35003 [12] Mathematical and Computer Modelling 18 pp 79– (1993) [13] Basel pp 359– (1994) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.