Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters
In the present paper we give conditions under which there exists a unique weak solution for a nonlocal equation driven by the integrodifferential operator of fractional Laplacian type. We argue for the optimality of some assumptions. Some Lyapunov-type inequalities are given. We also study the conti...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/7/851 |
| _version_ | 1797527150997274624 |
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| author | Robert Stegliński |
| author_facet | Robert Stegliński |
| author_sort | Robert Stegliński |
| collection | DOAJ |
| description | In the present paper we give conditions under which there exists a unique weak solution for a nonlocal equation driven by the integrodifferential operator of fractional Laplacian type. We argue for the optimality of some assumptions. Some Lyapunov-type inequalities are given. We also study the continuous dependence of the solution on parameters. In proofs we use monotonicity and variational methods. |
| first_indexed | 2024-03-10T09:39:56Z |
| format | Article |
| id | doaj.art-28eb8b17789a4ed3a713ff64a2815594 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T09:39:56Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-28eb8b17789a4ed3a713ff64a28155942023-11-22T03:44:46ZengMDPI AGEntropy1099-43002021-07-0123785110.3390/e23070851Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on ParametersRobert Stegliński0Institute of Mathematics, Lodz University of Technology, Wólczańska 215, 90-924 Lodz, PolandIn the present paper we give conditions under which there exists a unique weak solution for a nonlocal equation driven by the integrodifferential operator of fractional Laplacian type. We argue for the optimality of some assumptions. Some Lyapunov-type inequalities are given. We also study the continuous dependence of the solution on parameters. In proofs we use monotonicity and variational methods.https://www.mdpi.com/1099-4300/23/7/851monotone operatorunique solutionLyapunov-type inequalitiesdependence on parameters |
| spellingShingle | Robert Stegliński Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters Entropy monotone operator unique solution Lyapunov-type inequalities dependence on parameters |
| title | Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters |
| title_full | Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters |
| title_fullStr | Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters |
| title_full_unstemmed | Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters |
| title_short | Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters |
| title_sort | existence of a unique solution to a fractional partial differential equation and its continuous dependence on parameters |
| topic | monotone operator unique solution Lyapunov-type inequalities dependence on parameters |
| url | https://www.mdpi.com/1099-4300/23/7/851 |
| work_keys_str_mv | AT robertsteglinski existenceofauniquesolutiontoafractionalpartialdifferentialequationanditscontinuousdependenceonparameters |