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We consider the inverse nodal problem for Sturm-Liouville (S-L) equation with frozen argument. Asymptotic behaviours of eigenfunctions, nodal parameters are represented in two cases and numerical algorithms are produced to solve the given problems. Subsequently, solution of inverse nodal problem is calculated by the second Chebyshev wavelet method (SCW), accuracy and effectiveness of the method are shown in some numerical examples.

Some asymptotic formulae for spectra of a general convex domain.

E.M.E. Zayed (1988)

Collectanea Mathematica

Some classes of inverse evolution problems for parabolic equations.

Pyatkov, S.G., Tsybikov, B.N. (2009)

Sibirskij Matematicheskij Zhurnal

Some generalizations in the mathematical developments of the theory of the geodetic overdetermined problems.

F. Sacerdote, F. Sansò (1990)

Revista Matemática de la Universidad Complutense de Madrid

Two particular cases of the overdetermined gravimetry-gradiometry problem are discussed: (i) the case of a latitude-dependant statistical weight for gradiometric data, corresponding to a data distribution coming from satellite polar orbits, (ii) the case of a volume distribution, instead of a surface distribution, for satellite gradiometric data. In both cases a discussion of numerical methods for solving the problem with realistic data is started; for case (i), an analytic solution is found under...

Some Hölder-logarithmic estimates on Hardy-Sobolev spaces

Imed Feki, Ameni Massoudi (2024)

Czechoslovak Mathematical Journal

We prove some optimal estimates of Hölder-logarithmic type in the Hardy-Sobolev spaces $H^{k, p} (G)$ , where $k \in ℕ^{*}$ , $1 \leq p \leq \infty$ and $G$ is either the open unit disk $𝔻$ or the annular domain $G_{s}$ , $0 < s < 1$ of the complex space $ℂ$ . More precisely, we study the behavior on the interior of $G$ of any function $f$ belonging to the unit ball of the Hardy-Sobolev spaces $H^{k, p} (G)$ from its behavior on any open connected subset $I$ of the boundary $\partial G$ of $G$ with respect to the $L^{1}$ -norm. Our results can be viewed as an improvement and generalization of those established...

Some inverse and control problems for fluids

Enrique Fernández-Cara, Thierry Horsin, Henry Kasumba (2013)

Annales mathématiques Blaise Pascal

This paper deals with some inverse and control problems for the Navier-Stokes and related systems. We will focus on some particular aspects that have recently led to interesting (theoretical and numerical) results: geometric inverse problems, Eulerian and Lagrangian controllability and vortex reduction oriented to shape optimization.

Some mathematical problems in inverse potential scattering

A. Melin (1986/1987)

Séminaire Équations aux dérivées partielles (Polytechnique)

Some problems in inverse scattering theory

Anders Melin (1987)

Journées équations aux dérivées partielles

Some remarks on the multi-dimensional Borg-Levinson theorem

Hiroshi Isozaki (1989)

Journées équations aux dérivées partielles

Stability estimates for an inverse problem for the linear Boltzmann equation.

Rolci Cipolatti, Carlos M. Motta, Nilson C. Roberty (2006)

Revista Matemática Complutense

In this paper we consider the inverse problem of recovering the total extinction coefficient and the collision kernel for the time-dependent Boltzmann equation via boundary measurements. We obtain stability estimates for the extinction coefficient in terms of the albedo operator and also an identification result for the collision kernel.

Stability estimates of an inverse problem for the stationary transport equation

Jenn-Nan Wang (1999)

Annales de l'I.H.P. Physique théorique

Stability of a numerical method for solving the 3 D inverse scattering problem with fixed energy data.

A.G. Ramm (1991)

Journal für die reine und angewandte Mathematik

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