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- W3176924835 abstract "<p style='text-indent:20px;'>In this paper, we consider the following degenerate/singular parabolic equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE1> begin{document}$ begin{align*} u_t -(x^alpha u_{x})_x - frac{mu}{x^{2-alpha}} u = 0, qquad xin (0,1), t in (0,T), end{align*} $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id=M1>begin{document}$ 0leq alpha <1 $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=M2>begin{document}$ muleq (1-alpha)^2/4 $end{document}</tex-math></inline-formula> are two real parameters. We prove the boundary null controllability by means of a <inline-formula><tex-math id=M3>begin{document}$ H^1(0,T) $end{document}</tex-math></inline-formula> control acting either at <inline-formula><tex-math id=M4>begin{document}$ x = 1 $end{document}</tex-math></inline-formula> or at the point of degeneracy and singularity <inline-formula><tex-math id=M5>begin{document}$ x = 0 $end{document}</tex-math></inline-formula>. Besides we give sharp estimates of the cost of controllability in both cases in terms of the parameters <inline-formula><tex-math id=M6>begin{document}$ alpha $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=M7>begin{document}$ mu $end{document}</tex-math></inline-formula>. The proofs are based on the classical moment method by Fattorini and Russell and on recent results on biorthogonal sequences.</p>" @default.
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- W3176924835 date "2022-01-01" @default.
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- W3176924835 title "Existence and cost of boundary controls for a degenerate/singular parabolic equation" @default.
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- W3176924835 doi "https://doi.org/10.3934/mcrf.2021032" @default.
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