Inverse Problems of Simultaneous Determination of the Time-Dependent Right-Hand Side Term and the Coefficient in a Parabolic Equation

Камынин, В. Л.

doi:10.1007/978-3-319-20239-6_23

Cited by 5 publications

(6 citation statements)

References 4 publications

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“…В работах [13], [14] при дополнительных условиях типа (1.4) исследованы обратные задачи определения зависящих от 𝑡 неизвестного коэффициента перед 𝑢 и неизвестной правой части для параболических уравнений с одной и несколькими пространственными переменными, соответственно.…”

Section: в л камынинunclassified

Об Обратной Задаче Одновременного Определения Двух Зависящих От Времени Младших Коэффициентов В Недивергентном Параболическом Уравнении На Плоскости

Камынин¹,

Камынин

2020

Matematicheskie Zametki

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Доказаны теоремы существования и единственности решения обратной задачи одновременного определения зависящих от $t$ коэффициентов перед $u$ и $u_x$ в недивергентном параболическом уравнении с двумя независимыми переменными при условии интегрального наблюдения по $x$. Даны оценки максимумов модулей этих коэффициентов с константами, явно выписанными через входные данные задачи. Приведен пример обратной задачи, для которой применимы доказанные теоремы. Библиография: 19 названий.

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Section: в л камынинunclassified

Об Обратной Задаче Одновременного Определения Двух Зависящих От Времени Младших Коэффициентов В Недивергентном Параболическом Уравнении На Плоскости

Камынин¹,

Камынин

2020

Matematicheskie Zametki

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“…and therefore the inverse problem has at most one solution in the class of functions (15). In fact, it can easily be checked by direct substitution that the analytical solution is given by…”

Section: Examplementioning

confidence: 99%

“…[3,11], and recently been solved numerically by the authors, [8]. In these studies, the unknowns were mainly coefficients multiplying the temperature and its partial derivatives, but more recent theoretical studies, [14,15], allow for one of the time-dependent unknown to be in the free term heat source as well. And it is the purpose of this paper to numerically solve a couple of such related multiple coefficient identification problems.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous determination of time-dependent coefficients and heat source

Hussein

Lesnic

2016

International Journal for Computational Methods in Engineering

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This paper presents a numerical solution to the inverse problems of simultaneous determination of the time-dependent coefficients and the source term in the parabolic heat equation subject to overspecified conditions of integral type. The ill-posed problems are numerically discretised using the finite-difference method and the resulting system of nonlinear equations is solved numerically using the MATLAB toolbox routine lsqnonlin applied to minimizing the nonlinear Tikhonov regularization functional subject to simple physical bounds on the variables. Numerical examples are presented to illustrate the accuracy and stability of the solution.

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“…Indeed, we have only find works devoted to the simultaneous determination of source and coefficient, appearing in a parabolic equation, that depend only on the time variable (see e.g. [31,32]). In the same way, we are only aware of the work of [26] for the simultaneous determination of a source term and an obstacle appearing in a hyperbolic equation.…”

mentioning

confidence: 99%

Simultaneous determination of different class of parameters for a diffusion equation from a single measurement

Kian¹

2022

Inverse Problems

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This article is devoted to the simultaneous resolution of several inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single boundary measurement. Namely, we consider the simultaneous unique determination of several class of coefficients, some internal sources (a source term and an initial condition) and the fractional order in a diffusion equation from a single boundary measurement. Our problem can be formulated as the simultaneous determination of information about a diffusion process (velocity field, density of the medium) and of the source of diffusion. We consider this problems in the context of a classical diffusion process described by a convection-diffusion equation as well as an anomalous diffusion phenomena described by a time fractional diffusion equation.

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Inverse Problems of Simultaneous Determination of the Time-Dependent Right-Hand Side Term and the Coefficient in a Parabolic Equation

Cited by 5 publications

References 4 publications

Об Обратной Задаче Одновременного Определения Двух Зависящих От Времени Младших Коэффициентов В Недивергентном Параболическом Уравнении На Плоскости

Об Обратной Задаче Одновременного Определения Двух Зависящих От Времени Младших Коэффициентов В Недивергентном Параболическом Уравнении На Плоскости

Simultaneous determination of time-dependent coefficients and heat source

Simultaneous determination of different class of parameters for a diffusion equation from a single measurement

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