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Regularized solution for a biharmonic equation with discrete data
2019
Evolution Equations and Control Theory
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In this work, we focus on the Cauchy problem for the biharmonic equation associated with random data. In general, the problem is severely illposed in the sense of Hadamard, i.e, the solution does not depend continuously on the data. To regularize the instable solution of the problem, we apply a nonparametric regression associated with the Fourier truncation method. Also we will present a convergence result. 2000 Mathematics Subject Classification. 35K05, 35K99, 47J06, 47H10.
doi:10.3934/eect.2020008
fatcat:kb22toho7baqjnxvc4dlwtnipe