Geodesic
Reliable solution of parabolic obstacle problems with respect to uncertain data
Applications of Mathematics, Tome 48 (2003) no. 5, pp. 321-351.

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A class of parabolic initial-boundary value problems is considered, where admissible coefficients are given in certain intervals. We are looking for maximal values of the solution with respect to the set of admissible coefficients. We give the abstract general scheme, proposing how to solve such problems with uncertain data. We formulate a general maximization problem and prove its solvability, provided all fundamental assumptions are fulfilled. We apply the theory to certain Fourier obstacle type maximization problem.
DOI : 10.1023/B:APOM.0000024480.06960.ea
Classification : 35B30, 35K85, 49J40
Keywords: uncertain data; optimal design approach; parabolic obstacle problems; penalization method; Fourier problem 
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     title = {Reliable solution of parabolic obstacle problems with respect to uncertain data},
     journal = {Applications of Mathematics},
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Lovíšek, Ján. Reliable solution of parabolic obstacle problems with respect to uncertain data. Applications of Mathematics, Tome 48 (2003) no. 5, pp. 321-351. doi : 10.1023/B:APOM.0000024480.06960.ea. http://geodesic.mathdoc.fr/articles/10.1023/B:APOM.0000024480.06960.ea/

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