Existence and uniqueness results for an inverse problem for semilinear parabolic equations

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1057-1064 ◽  
Author(s):  
Ali Sazaklioglu ◽  
Allaberen Ashyralyev ◽  
Abdullah Erdogan
Keyword(s):  
Inverse Problem ◽  
Difference Scheme ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Semilinear Parabolic Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Accuracy Difference ◽  
Integral Overdetermination ◽  
Semilinear Parabolic

In the present study, unique solvability of an inverse problem governed by semilinear parabolic equations with an integral overdetermination is investigated. Furthermore, for the approximate solution of this problem a first order of accuracy difference scheme is constructed. Existence and uniqueness results for the solution of this difference scheme are established. Considering a particular example, some numerical results are discussed.

scholarly journals Existence and uniqueness results for an inverse problem for a semilinear equation with final overdetermination

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 847-858 ◽  
Author(s):  
Ali Sazaklioglu ◽  
Abdullah Erdogan ◽  
Allaberen Ashyralyev
Keyword(s):  
Banach Space ◽  
Inverse Problem ◽  
Difference Scheme ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Order Of Accuracy ◽  
First Order ◽  
Existence And Uniqueness Results ◽  
Semilinear Equation ◽  
Uniqueness Results

In the present paper, unique solvability of a source identification inverse problem for a semilinear equation with a final overdetermination in a Banach space is investigated. Moreover, the first order of accuracy Rothe difference scheme is presented for numerically solving this problem. The existence and uniqueness result for this difference scheme is given. The efficiency of the proposed method is evaluated by means of computational experiments.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

scholarly journals BSDEs with polynomial growth generators

2000 ◽  
Vol 13 (3) ◽  
pp. 207-238 ◽  
Author(s):  
Philippe Briand ◽  
René Carmona
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Polynomial Growth ◽  
Probabilistic Representation ◽  
Existence And Uniqueness Results ◽  
State Variable ◽  
Cahn Equation ◽  
Uniqueness Results ◽  
Terminal Time

In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.

Nontrivial solutions of non-autonomous dirichlet fractional discrete problems

2020 ◽  
Vol 23 (4) ◽  
pp. 980-995
Author(s):  
Alberto Cabada ◽  
Nikolay Dimitrov
Keyword(s):  
Existence And Uniqueness ◽  
Point Boundary ◽  
Nontrivial Solutions ◽  
Fractional Difference ◽  
Nonlinear Part ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Difference Equation ◽  
Discrete Problems ◽  
Series Of Functions

AbstractIn this paper, we introduce a two-point boundary value problem for a finite fractional difference equation with a perturbation term. By applying spectral theory, an associated Green’s function is constructed as a series of functions and some of its properties are obtained. Under suitable conditions on the nonlinear part of the equation, some existence and uniqueness results are deduced.

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