Reconstruction and stability of inverse nodal problems for energy-dependent p-Laplacian equations

Cheng, Yan-Hsiou

doi:10.1016/j.jmaa.2020.124388

Cited by 3 publications

(4 citation statements)

References 13 publications

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“…Cheng [47] investigated inverse nodal problems for energy‐dependent

p

‐Laplacian equations and of the study applies the Tikhonov regularization method to reconstruct potential functions by only using zeros of one eigenfunction and show that the space of the

p

‐Laplacian operator is homeomorphic to the partition set of the space of nodal sequences.…”

Section: Inverse Nodal Problemsmentioning

confidence: 99%

Inverse nodal problems for singular diffusion equation

Amirov,

Durak

2024

Math Methods in App Sciences

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In this study, some properties of the pencils of singular Sturm–Liouville operators are investigated. Firstly, the behaviors of eigenvalues and eigenfunctions is learned, then for each discontinuity point a solution of the inverse problem is given to determine the potential function and parameters , and with the help of a dense set of nodes. And finally, a constructive method is given for solving the given inverse problem.

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“…Cheng [47] investigated inverse nodal problems for energy‐dependent

p

‐Laplacian equations and of the study applies the Tikhonov regularization method to reconstruct potential functions by only using zeros of one eigenfunction and show that the space of the

p

‐Laplacian operator is homeomorphic to the partition set of the space of nodal sequences.…”

Section: Inverse Nodal Problemsmentioning

confidence: 99%

Inverse nodal problems for singular diffusion equation

Amirov,

Durak

2024

Math Methods in App Sciences

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“…In this section, the solution of the nodal inverse problem for the diffusion operator with p(x) = βδ (x − a)-Dirac delta potential and any of the set of nodal points dense in the interval (0, π) of the constants β, h, H and q(x) function, an algorithm for determining with the help of subsequence will be given. Such problems have been studied in studies of [3,12,[20][21][22] for the regular diffusion operator.…”

Section: Inverse Nodal Problemsmentioning

confidence: 99%

“…In the [20] investigate inverse nodal problems for energy-dependant p-Laplacian equations and of the study applies the Tikhonov regularization method to reconstruct potential functions by only using zeros of one eigenfunction and show that the space of the p-Laplacian operator is homeomorphic to the partition set of the space of nodal sequences. Now, we examine the case of a = π 2 and H = +∞ for the sake of simplicity.…”

Section: Inverse Nodal Problemsmentioning

confidence: 99%

Spectral Properties and Inverse Nodal Problems for Singular Diffusion Equation

AMİROV,

DURAK

2024

Hacettepe Journal of Mathematics and Statistics

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In this study, some properties for the pencils of singular Sturm-Liouville operators are investigated. Firstly, the behaviors of eigenvalues were learned, then the solutions of the inverse problem were given to determine the potential function and parameters of the boundary condition with the help of a dense set of nodal points and lastly we obtain a constructive solution to the inverse problems of this class.

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“…We now recollect some literature on the studying of p-Laplacian equation. This equation arises naturally in a boundary value problem of partial differential equations and has been widely used in various fields of science and technology; see [2,7,8] and the references therein. In the absence of noise, that is a deterministic p-Laplacian equations, many studies have been done on various aspects of attractors.…”

mentioning

confidence: 99%

Regularity of Wong-Zakai approximation for non-autonomous stochastic quasi-linear parabolic equation on <inline-formula><tex-math id="M1">$ {\mathbb{R}}^N $</tex-math></inline-formula>

Liu

Zhao

2021

era

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<p style='text-indent:20px;'>In this paper, we investigate a non-autonomous stochastic quasi-linear parabolic equation driven by multiplicative white noise by a Wong-Zakai approximation technique. The convergence of the solutions of quasi-linear parabolic equations driven by a family of processes with stationary increment to that of stochastic differential equation with white noise is obtained in the topology of <inline-formula><tex-math id="M2">\begin{document}$ L^2( {\mathbb{R}}^N) $\end{document}</tex-math></inline-formula> space. We establish the Wong-Zakai approximations of solutions in <inline-formula><tex-math id="M3">\begin{document}$ L^l( {\mathbb{R}}^N) $\end{document}</tex-math></inline-formula> for arbitrary <inline-formula><tex-math id="M4">\begin{document}$ l\geq q $\end{document}</tex-math></inline-formula> in the sense of upper semi-continuity of their random attractors, where <inline-formula><tex-math id="M5">\begin{document}$ q $\end{document}</tex-math></inline-formula> is the growth exponent of the nonlinearity. The <inline-formula><tex-math id="M6">\begin{document}$ L^l $\end{document}</tex-math></inline-formula>-pre-compactness of attractors is proved by using the truncation estimate in <inline-formula><tex-math id="M7">\begin{document}$ L^q $\end{document}</tex-math></inline-formula> and the higher-order bound of solutions.</p>

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Reconstruction and stability of inverse nodal problems for energy-dependent p-Laplacian equations

Cited by 3 publications

References 13 publications

Inverse nodal problems for singular diffusion equation

Inverse nodal problems for singular diffusion equation

Spectral Properties and Inverse Nodal Problems for Singular Diffusion Equation

Regularity of Wong-Zakai approximation for non-autonomous stochastic quasi-linear parabolic equation on <inline-formula><tex-math id="M1">$ {\mathbb{R}}^N $</tex-math></inline-formula>

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