Globally linearizing control of linear time-fractional diffusion-advection-reaction systems

2022 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Jean Pierre Corriou ◽  
Ahmed MAIDI
Keyword(s):  
Linear Time ◽  
Fractional Diffusion ◽  
Reaction Systems

scholarly journals Verification of Linear-Time Temporal Properties for Reaction Systems with Discrete Concentrations

2017 ◽  
Vol 154 (1-4) ◽  
pp. 289-306 ◽  
Author(s):  
Artur Męski ◽  
Maciej Koutny ◽  
Wojciech Penczek
Keyword(s):  
Linear Time ◽  
Reaction Systems ◽  
Temporal Properties

scholarly journals Uniqueness for an inverse source problem of determining a space-dependent source in a non-autonomous time-fractional diffusion equation

2020 ◽  
Vol 23 (6) ◽  
pp. 1702-1711
Author(s):  
Marian Slodička
Keyword(s):  
Source Term ◽  
Linear Time ◽  
Fractional Diffusion ◽  
Time Measurement ◽  
Uniqueness Result ◽  
Inverse Source Problem ◽  
Final Time ◽  
Fractional Diffusion Equations ◽  
Time Fractional Diffusion Equation ◽  
Uniqueness Of A Solution

Abstract We study uniqueness of a solution for an inverse source problem arising in linear time-fractional diffusion equations with time-dependent coefficients. We consider source term in a separated form h(t)f (x). The unknown source f (x) is recovered from the final time measurement u (x, T). A new uniqueness result is formulated in Theorem 3.1 under the assumption that h ∈ C ([0, T]) and 0 ≢ h ≥ 0. No monotonicity in time for h(t) and for coefficients of the differential operator is required.

scholarly journals Well-posedness results and blow-up for a semi-linear time fractional diffusion equation with variable coefficients

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Vo Van Au ◽  
Jagdev Singh ◽  
Anh Tuan Nguyen
Keyword(s):  
Diffusion Equation ◽  
Blow Up ◽  
Linear Time ◽  
Unique Continuation ◽  
Fractional Diffusion ◽  
Variable Coefficients ◽  
Fractional Diffusion Equation ◽  
Well Posedness ◽  
Regularity Estimates ◽  
Logarithmic Functions

<p style='text-indent:20px;'>The semi-linear problem of a fractional diffusion equation with the Caputo-like counterpart of a hyper-Bessel differential is considered. The results on existence, uniqueness and regularity estimates (local well-posedness) of the solutions are established in the case of linear source and the source functions that satisfy the globally Lipschitz conditions. Moreover, we prove that the problem exists a unique positive solution. In addition, the unique continuation of solutions and a finite-time blow-up are proposed with the reaction terms are logarithmic functions.</p>

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