Unique solvability of some inverse problems of sorption dynamics with a linear isotherm

1990 ◽  
Vol 1 (3) ◽  
pp. 281-283
Author(s):  
A. M. Denisov ◽  
I. V. Podlevskikh
Keyword(s):  
Inverse Problems ◽  
Unique Solvability ◽  
Linear Isotherm ◽  
Sorption Dynamics

Inverse source problem for parabolic equation with the condition of integral observation in time

2018 ◽  
Vol 26 (4) ◽  
pp. 523-539 ◽  
Author(s):  
Aleksey I. Prilepko ◽  
Vitaly L. Kamynin ◽  
Andrew B. Kostin
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Inverse Problems ◽  
Unique Solvability ◽  
Existence And Uniqueness ◽  
Additional Condition ◽  
Sufficient Conditions ◽  
Inverse Source Problem ◽  
Source Determination ◽  
Integral Observation

Abstract We consider the inverse problem of source determination in nonuniformly parabolic equation under the additional condition of integral observation. We investigate the questions of existence and uniqueness of solution. Two types of sufficient conditions for the unique solvability of the inverse problem are obtained. Examples of inverse problems are given for which the conditions of the proved theorems are fulfilled.

scholarly journals Direct and Inverse Problems for Sturm-Liouville Operator Which Has Discontinuity Conditions and Coulomb Potential

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Yalçın Güldü ◽  
Merve Arslantaş
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Unique Solvability ◽  
Coulomb Potential ◽  
Liouville Operator ◽  
Direct And Inverse Problems ◽  
Main Equation ◽  
Sturm Liouville ◽  
Discontinuity Conditions

We give a derivation of the main equation for Sturm-Liouville operator with Coulomb potential and prove its unique solvability. Using the solution of the main equation, we get an algorithm for the solution of the inverse problem.

Inverse problems for a class of degenerate evolution equations with Riemann – Liouville derivative

2019 ◽  
Vol 22 (2) ◽  
pp. 271-286 ◽  
Author(s):  
Vladimir E. Fedorov ◽  
Roman R. Nazhimov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Unique Solvability ◽  
Sufficient Conditions ◽  
Well Posedness ◽  
Cauchy Type ◽  
Liouville Derivative

Abstract Unique solvability and well-posedness issues are studied for linear inverse problems with a constant unknown parameter to fractional order differential equations with Riemann – Liouvlle derivative in Banach spaces. Firstly, well-posedness criteria for the inverse problem with the Cauchy type initial conditions to the differential equation in a Banach space that solved with respect to the fractional derivative is obtained. This result is applied to search of sufficient conditions for the unique solution existence of the inverse problem for equation with linear degenerate operator at the Riemann – Liouville fractional derivative. It is shown that the presence of the matching conditions for the data of the problem excludes the possibility of the well-posedness consideration for the degenerate inverse problem with the Cauchy type condition. But for the inverse problem with the Showalter – Sidorov type conditions it is found the criteria of the well-posedness. Abstract results are used to the search of conditions of the unique solvability for an inverse problem to a class of partial differential equations of time-fractional order with polynomials of elliptic differential operators with respect to the spatial variables.

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