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Applicable Analysis
An International Journal
Volume 19, 1985 - Issue 2-3
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Original Articles

Improved Stability Estimates for Classes of Illposed Cauchy Problems

L. E. PayneView further author information
Pages 63-74 | Published online: 02 May 2007

Citations (27)

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Dinh Nho Hào & H.-J. Reinhardt. (1998) Gradient methods for inverse heat conduction problems. Inverse Problems in Engineering 6:3, pages 177-211.
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H.-J. Reinhardt & Dinh Nho Hào. (1996) A sequential conjugate gradient method for the stable numerical solution to inverse heat conduction problems. Inverse Problems in Engineering 2:4, pages 263-272.
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Articles from other publishers (25)

Xiaoli Feng & Lars Eldén. (2014) Solving a Cauchy problem for a 3D elliptic PDE with variable coefficients by a quasi-boundary-value method. Inverse Problems 30:1, pages 015005.
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Xian Zheng Jia. (2011) A Holder Type Estimate for an ill-Posed Cauchy Problem for the 3-D Heat Equation. Advanced Materials Research 422, pages 589-591.
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Xiao-Li Feng, Chu-Li Fu & Hao Cheng. (2011) A regularization method for solving the Cauchy problem for the Helmholtz equation. Applied Mathematical Modelling 35:7, pages 3301-3315.
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Xiang-Tuan Xiong. (2010) On a radially symmetric inverse heat conduction problem. Applied Mathematical Modelling 34:2, pages 520-529.
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Rolando Magnanini & Giorgio Talenti. (2009) On Complex-valued 2D Eikonals. Part Four: Continuation Past a Caustic. Milan Journal of Mathematics 77:1, pages 1-66.
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Sergio Vessella. 2009. Handbook of Differential Equations - Evolutionary Equations. Handbook of Differential Equations - Evolutionary Equations 421 500 .
Sergio Vessella. (2008) Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates. Inverse Problems 24:2, pages 023001.
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Lars Eldén & Fredrik Berntsson. (2005) A stability estimate for a Cauchy problem for an elliptic partial differential equation. Inverse Problems 21:5, pages 1643-1653.
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J.R. Dorroh & Xueping Ru. (1999) The Application of the Method of Quasi-reversibility to the Sideways Heat Equation. Journal of Mathematical Analysis and Applications 236:2, pages 503-519.
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H.S. Oster & Y. Rudy. (1997) Regional regularization of the electrocardiographic inverse problem: a model study using spherical geometry. IEEE Transactions on Biomedical Engineering 44:2, pages 188-199.
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. 1997. Non-Standard and Improperly Posed Problems. Non-Standard and Improperly Posed Problems 284 300 .
Karen A. Ames & Brian Straughan. 1997. Non-Standard and Improperly Posed Problems. Non-Standard and Improperly Posed Problems 217 237 .
Karen A. Ames & Brian Straughan. 1997. Non-Standard and Improperly Posed Problems. Non-Standard and Improperly Posed Problems 1 33 .
Diego A. Murio. 1993. The Mollification Method and the Numerical Solution of Ill-Posed Problems. The Mollification Method and the Numerical Solution of Ill-Posed Problems 232 248 .
A. Morro & B. Straughan. (1992) Continuous dependence on the source parameters for convective motion in porous media. Nonlinear Analysis: Theory, Methods & Applications 18:4, pages 307-315.
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Karen A. Ames. 1992. Nonlinear Equations in the Applied Sciences. Nonlinear Equations in the Applied Sciences 1 29 .
Dinh Nho Hào & Rudolf Gorenflo. (1991) A noncharacteristic cauchy problem for the heat equation. Acta Applicandae Mathematicae 24:1, pages 1-27.
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A. Morro & B. Straughan. (2005) A uniqueness theorem in the dynamical theory of piezoelectricity. Mathematical Methods in the Applied Sciences 14:5, pages 295-299.
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L.E. Payne & B. Straughan. (1990) Error estimates for the temperature of a piece of cold ice, given data on only part of the boundary. Nonlinear Analysis: Theory, Methods & Applications 14:5, pages 443-452.
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Peter Knabner & Sergio Vessella. (2005) The optimal stability estimate for some ill‐posed Cauchy problems for a parabolic equation. Mathematical Methods in the Applied Sciences 10:5, pages 575-583.
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Peter Knabner & Sergio Vessella. (1987) Stabilization of ill-posed Cauchy problems for parabolic equations. Annali di Matematica Pura ed Applicata 149:1, pages 393-409.
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Karen A. Ames, Howard A. Levine & Lawrence E. Payne. 1987. Inverse and Ill-Posed Problems. Inverse and Ill-Posed Problems 443 450 .
Peter Knabner & Sergio Vessella. 1987. Inverse and Ill-Posed Problems. Inverse and Ill-Posed Problems 351 368 .
Lars Eldén. 1987. Inverse and Ill-Posed Problems. Inverse and Ill-Posed Problems 345 350 .
Peter Monk. (1986) Error Estimates for a Numerical Method for an Ill-Posed Cauchy Problem for the Heat Equation. SIAM Journal on Numerical Analysis 23:6, pages 1155-1172.
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