scholarly journals On an inverse problem for fractional evolution equation

2017 ◽  
Vol 6 (1) ◽  
pp. 111-134
Author(s):  
Nguyen Huy Tuan ◽  
◽  
Mokhtar Kirane ◽  
Long Dinh Le ◽  
Van Thinh Nguyen ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Evolution Equation ◽  
Fractional Evolution Equation

scholarly journals A priori bounds of the solution of a one point IBVP for a singular fractional evolution equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Said Mesloub ◽  
Hassan Eltayeb Gadain
Keyword(s):  
Differential Equations ◽  
Evolution Equation ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Initial Boundary ◽  
A Priori Bounds ◽  
Fractional Evolution Equation ◽  
Priori Estimates ◽  
Initial Boundary Value

Abstract A priori bounds constitute a crucial and powerful tool in the investigation of initial boundary value problems for linear and nonlinear fractional and integer order differential equations in bounded domains. We present herein a collection of a priori estimates of the solution for an initial boundary value problem for a singular fractional evolution equation (generalized time-fractional wave equation) with mass absorption. The Riemann–Liouville derivative is employed. Results of uniqueness and dependence of the solution upon the data were obtained in two cases, the damped and the undamped case. The uniqueness and continuous dependence (stability of solution) of the solution follows from the obtained a priori estimates in fractional Sobolev spaces. These spaces give what are called weak solutions to our partial differential equations (they are based on the notion of the weak derivatives). The method of energy inequalities is used to obtain different a priori estimates.

An inverse problem for an evolution equation

1991 ◽  
Vol 49 (5) ◽  
pp. 535-540 ◽  
Author(s):  
Yu. S. �idel'man
Keyword(s):  
Inverse Problem ◽  
Evolution Equation

scholarly journals Decay of mass for fractional evolution equation with memory term

2012 ◽  
Vol 71 (2) ◽  
pp. 215-228 ◽  
Author(s):  
Ahmad Z. Fino ◽  
Hassan Ibrahim ◽  
Bilal Barakeh
Keyword(s):  
Evolution Equation ◽  
Memory Term ◽  
Fractional Evolution Equation ◽  
With Memory

scholarly journals An Inverse Problem for a Class of Linear Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25
Author(s):  
Yuhuan Zhao
Keyword(s):  
Inverse Problem ◽  
Evolution Equation ◽  
Evolution Equations ◽  
Optimal Parameter ◽  
Optimization Method ◽  
Necessary Condition ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Fréchet Differentiable

An inverse problem for a linear stochastic evolution equation is researched. The stochastic evolution equation contains a parameter with values in a Hilbert space. The solution of the evolution equation depends continuously on the parameter and is Fréchet differentiable with respect to the parameter. An optimization method is provided to estimate the parameter. A sufficient condition to ensure the existence of an optimal parameter is presented, and a necessary condition that the optimal parameter, if it exists, should satisfy is also presented. Finally, two examples are given to show the applications of the above results.

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