An inverse problem of finding a parameter in a semi-linear heat equation

Cannon, John R.; Yong, Lin

doi:10.1016/0022-247x(90)90414-b

Cited by 136 publications

(59 citation statements)

References 5 publications

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“…This result was extended to three dimension heat equation in [8]. The case of a non local measurement was considered by Canon and Lin in [9,10]. In [12], the first author proved existence, uniqueness and Lipschitz stability for the determination of a time-dependent coefficient appearing in an abstract integro-differential equation, extending earlier results in [13].…”

Section: 3)mentioning

confidence: 58%

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Logarithmic stability in determining the time-dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to-Neumann map. Application to the determination of a nonlinear term

Choulli

Kian

2018

Journal de Mathématiques Pures et Appliquées

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Abstract. We give a new stability estimate for the problem of determining the time-dependent zero order coefficient in a parabolic equation from a partial parabolic Dirichlet-to-Neumann map. The novelty of our result is that, contrary to the previous works, we do not need any measurement on the final time. We also show how this result can be used to establish a stability estimate for the problem of determining the nonlinear term in a semilinear parabolic equation from the corresponding "linearized" Dirichlet-to-Neumann map. The key ingredient in our analysis is a parabolic version of an elliptic Carleman inequality due to Bukhgeim and Uhlmann [6]. This parabolic Carleman inequality enters in an essential way in the construction of CGO solutions that vanish at a part of the lateral boundary.

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Section: 3)mentioning

confidence: 58%

“…On the other hand 10) where c 1 is a constant depending only on Q. This interpolation inequality is more or less known but, for sake of completeness, we provide its proof in Lemma B.1 of Appendix B.…”

Section: In Light Of [Theorem 54 Page 322 Lsu] the Ibvp Has A Uniqmentioning

confidence: 99%

Logarithmic stability in determining the time-dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to-Neumann map. Application to the determination of a nonlinear term

Choulli

Kian

2018

Journal de Mathématiques Pures et Appliquées

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“…We want to identify the control function p(t) that will yield a desired energy prescribed in a portion of the spatial domain. Some application of inverse problem (1.1)-(1.5) can be found in [4,5,8,9].…”

Section: U(x T)dx = E(t)mentioning

confidence: 99%

Solution of a semilinear parabolic equation with an unknown control function using the decomposition procedure of Adomian

Dehghan

Tatari

2006

Numerical Methods Partial

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The investigation of nonclassical parabolic initial-boundary value problems, which involve an integral over the spatial domain of a function of the desired solution, is of considerable concern. In this article a parabolic partial differential equation subject to energy overspecification is studied. This problem is appeared in modeling of many physical phenomena. The Adomian decomposition method, which is an efficient method for solving various class of problems, is employed for solving this model. This method provides an analytical solution in terms of an infinite convergent power series. Some examples are reported to support the simplicity of the decomposition procedure of Adomian.

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“…Certain types of physical problems can be modeled by Eqs. (1)- (5) by many authors (see for example [1,[3][4][5][6]8], and the references therein). Eq.…”

Section: Introductionmentioning

confidence: 99%

Cardinal Hermite interpolant multiscaling functions for solving a parabolic inverse problem

Ashpazzadeh¹,

Lakestani²,

Razzaghi³

2017

Turk J Math

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An effective method based upon cardinal Hermite interpolant multiscaling functions is proposed for the solution of the one-dimensional parabolic partial differential equation with given initial condition and known boundary conditions and subject to overspecification at a point in the spatial domain. The properties of multiscaling functions are first presented. These properties together with a collocation method are then utilized to reduce the parabolic inverse problem to the solution of algebraic equations. The scheme described is efficient. The numerical results obtained using the present algorithms for test problems show that this method can solve the model effectively.

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An inverse problem of finding a parameter in a semi-linear heat equation

Cited by 136 publications

References 5 publications

Logarithmic stability in determining the time-dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to-Neumann map. Application to the determination of a nonlinear term

Logarithmic stability in determining the time-dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to-Neumann map. Application to the determination of a nonlinear term

Solution of a semilinear parabolic equation with an unknown control function using the decomposition procedure of Adomian

Cardinal Hermite interpolant multiscaling functions for solving a parabolic inverse problem

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