Existence and cost of boundary controls for a degenerate/singular parabolic equation
نویسندگان
چکیده
<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 x\in (0,1), \ t \in (0,T), \end{align*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ 0\leq \alpha &lt;1 $\end{document}</tex-math></inline-formula> and id="M2">\begin{document}$ \mu\leq (1-\alpha)^2/4 are two real parameters. We prove boundary null controllability by means of a id="M3">\begin{document}$ H^1(0,T) control acting either at id="M4">\begin{document}$ x 1 or point degeneracy singularity id="M5">\begin{document}$ 0 $\end{document}</tex-math></inline-formula>. Besides give sharp estimates cost in both cases terms parameters id="M6">\begin{document}$ id="M7">\begin{document}$ \mu The proofs based on classical moment method Fattorini Russell recent results biorthogonal sequences.</p>
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ژورنال
عنوان ژورنال: Mathematical Control and Related Fields
سال: 2022
ISSN: ['2156-8499', '2156-8472']
DOI: https://doi.org/10.3934/mcrf.2021032