2022
DOI: 10.3934/cpaa.2022043
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Hölder-Logarithmic type approximation for nonlinear backward parabolic equations connected with a pseudo-differential operator

Abstract: <p style='text-indent:20px;'>In this paper, we deal with the backward problem for nonlinear parabolic equations involving a pseudo-differential operator in the <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula>-dimensional space. We prove that the problem is ill-posed in the sense of Hadamard, i.e., the solution, if it exists, does not depend continuously on the data. To regularize the problem, we propose two modified versions of the … Show more

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