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Inverse problems for fractional diffusion equations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Inverse problems for fractional diffusion equationsby Durdimurod K. Durdiev.
作者:	Durdiev, Durdimurod K.
出版者:	Singapore :Springer Nature Singapore :2025.
面頁冊數:	xiv, 295 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Inverse problems (Differential equations)
電子資源:	https://doi.org/10.1007/978-981-96-5338-6
ISBN:	9789819653386$q(electronic bk.)

Inverse problems for fractional diffusion equations
Durdiev, Durdimurod K.

Inverse problems for fractional diffusion equations[electronic resource] /by Durdimurod K. Durdiev. - Singapore :Springer Nature Singapore :2025. - xiv, 295 p. :ill., digital ;24 cm. - Industrial and applied mathematics,2364-6845. - Industrial and applied mathematics..

Coeffcient Determination Problems with Local Boundary and Overdetermination Conditions -- Inverse Coeffcient Problems with Nonlocal Initial and Integral Overdetermination Conditions -- Coeffcient Determination Problems with Cauchy and Overdetermination Conditions -- Carleman Estimate Method in Inverse Problems for a Fractional Diffusion Equation -- Determination of Source and Initial Functions -- Convolution Kernel Determination Problems in Fractional Diffusion Equations -- Determining Two Unknown Functions in a Fractional Diffusion Equation.

This book discusses various inverse problems for the time-fractional diffusion equation, such as inverse coefficient problems (nonlinear problems) and inverse problems for determining the right-hand sides of equations and initial functions (linear problems). The study of inverse problems requires a comprehensive investigation of direct problems (such as representation formulas, a priori estimates and differential properties of the solution). This is particularly evident in nonlinear problems, where obtaining solvability theorems necessitates careful tracking of the exact dependence of the differential properties of the solution to the direct problem on the smoothness of the coefficients and other problem data. Therefore, a significant portion of the book is devoted to direct problems, such as initial problems (Cauchy problems) and initial-boundary value problems with various boundary conditions.

ISBN: 9789819653386$q(electronic bk.)

Standard No.: 10.1007/978-981-96-5338-6doiSubjects--Topical Terms:

189581
Inverse problems (Differential equations)

LC Class. No.: QA378.5

Dewey Class. No.: 515.357

Inverse problems for fractional diffusion equations
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505 0 $a Coeffcient Determination Problems with Local Boundary and Overdetermination Conditions -- Inverse Coeffcient Problems with Nonlocal Initial and Integral Overdetermination Conditions -- Coeffcient Determination Problems with Cauchy and Overdetermination Conditions -- Carleman Estimate Method in Inverse Problems for a Fractional Diffusion Equation -- Determination of Source and Initial Functions -- Convolution Kernel Determination Problems in Fractional Diffusion Equations -- Determining Two Unknown Functions in a Fractional Diffusion Equation.
520 $a This book discusses various inverse problems for the time-fractional diffusion equation, such as inverse coefficient problems (nonlinear problems) and inverse problems for determining the right-hand sides of equations and initial functions (linear problems). The study of inverse problems requires a comprehensive investigation of direct problems (such as representation formulas, a priori estimates and differential properties of the solution). This is particularly evident in nonlinear problems, where obtaining solvability theorems necessitates careful tracking of the exact dependence of the differential properties of the solution to the direct problem on the smoothness of the coefficients and other problem data. Therefore, a significant portion of the book is devoted to direct problems, such as initial problems (Cauchy problems) and initial-boundary value problems with various boundary conditions.
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