Inverse Problems for Fractional Diffusion Equations / / by Durdimurod K. Durdiev

• Record Nr.: UNINA9911010526103321
• Autore: Durdiev Durdimurod K
• Pubbl/distr/stampa: Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2025
• ISBN: 981-9653-38-X
• Edizione: [1st ed. 2025.]
• Descrizione fisica: 1 online resource (476 pages)
• Collana: Industrial and Applied Mathematics, , 2364-6845
• Disciplina: 515.625; 515.75
• Soggetti: Difference equations; Functional equations; Difference and Functional Equations; Equacions diferencials; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: 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.
• Sommario/riassunto: 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.