Inverse Problems for Fractional Diffusion Equations
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Beschreibung
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.
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.
Discusses the challenges of using observed data to estimate the values of unknown parameters to characterize a system Highlights the direct problems, such as initial problems (Cauchy problems) and initial-boundary value problems Presents new results on determining coefficients, convolution kernels and right-hand sides of time-fractional diffusion
Autor*in
Durdimurod K. Durdiev
Themen in »Inverse Problems for Fractional Diffusion Equations«
inverse problems fractional diffusion equations boundary value problem Cauchy problem overdetermination condition uniqueness global solvability Coeffcient determination problems Carleman estimate method Holder stability Lipschitz stability convolution kernel determination problems