Maximum principle for the generalized time-fractional diffusion equation

By Yury F. Luchko. 2009

361 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2630377d7b5294c4d77448272cc8c9f8cc890f32

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation (2011, positive): “In particular, the global boundedness of appropriately defined weak solutions and a maximum principle for the weak solutions of such equations were established by employing a different technique compared to the one used in the papers [20,21].”
Overview to mathematical analysis for fractional diffusion equations - new mathematical aspects motivated by industrial collaboration (2010, background): “Moreover in Luchko [25], the following is proved.”
Time fractional diffusion equations: solution concepts, regularity, and long-time behavior (2019, result): “Results on the maximum principle in a stronger setting have also been found in [28, 29] by different methods.”
Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems (2011, background): “In Luchko [22], the maximum principle for an initial value/boundary value problem is established.”
Numerical methods for time-fractional evolution equations with nonsmooth data: A concise overview (2018, background): “, [5, 21, 71, 88, 74, 90, 55, 46, 4, 65, 101, 25]; see also the monograph [87] for closely related evolutionary integral equations.”
Spectral Optimization Methods for the Time Fractional Diffusion Inverse Problem (2013, background): “Luchko [12, 13] derived the maximum principle and proved the unique existence of the generalized solution.”
Coefficient inverse problem for a fractional diffusion equation (2013, background): “3) has been studied recently and we can refer to [25, 27, 28, 34].”
Maximum Principles for Multi-Term Space-Time Variable-Order Fractional Diffusion Equations and their Applications (2016, background): “Luchko in [10] proved a maximum principle for a generalized time-fractional diffusion equation.”
Maximum principle for the fractional diffusion equations with the Riemann-Liouville fractional derivative and its applications (2014, background): “The main reason for this choice of the fractional derivative is connected with the fact that the Caputo fractional derivative possesses a kind of an extremum principle that says that the Caputo fractional derivative of the order α, 0 < α ≤ 1 at the maximum point of a continuous function on some clos”
BOUNDARY VALUE PROBLEMS FOR THE GENERALIZED TIME-FRACTIONAL DIFFUSION EQUATION OF DISTRIBUTED ORDER (2009, methodology): “In particular, the global boundedness of appropriately defined weak solutions and a maximum principle for the weak solutions of such equations were established in [25] by employing a different technique compared to the one used in the papers [13], [14].”
Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation (2011, neutral): “For the proofs of results we refer the readers to [13] and [14].”
Inverse source problem for a fractional diffusion equation (2011, background): “For instance in Luchko [17], maximum principle for an initial value/boundary value problem was obtained and in Luchko [18], the unique existence of the generalized solution was followed directly.”
Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation (2013, methodology): “For a well-posedness analysis, we refer to [10, 13, 14, 31, 32, 35, 43].”
Well-posedness of general Caputo-type fractional differential equations (2018, methodology): “Luchko [13] first formulated a maximum principle for the time-fractional diffusion equation with the Caputo derivative and used the principle to obtain a uniqueness result for classical solutions.”
Time-fractional diffusion equation in the fractional Sobolev spaces (2015, background): “We mention here also the papers [3], [14], [16]-[19], [25], where some recent developments regarding the partial fractional differential equations are presented.”
General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems (2016, methodology): “These inequalities were proved in [1] and [15], respectively.”
Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation (2009, background): “There are many works on the forward problem for fractional diffusion equations such as an initial value/boundary value problem, and we refer to Bazhlekova [2], Eidelman and Kochubei [6], Metzler and Klafter [27], Gorenflo et al [10], Hanyga [12], Luchko [19, 20] and references therein; see also Prüs”
Maximum principle for certain generalized time and space fractional diffusion equations (2015, background): “MR2595950 (2010k:35515) [23] Yuri Luchko, Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation, Fract.”
Well-posedness of Hamilton–Jacobi equations with Caputo’s time fractional derivative (2016, background): “He established a maximum principle for Caputo’s fractional derivative in [30] and, based on it, proved a uniqueness of classical solutions for an initial-boundary value problem of (1.”