Wellposedness of Second Order Evolution Equations
In this paper we study a mild wellposedness notion of a second-order abstract differential equation defined in the whole line. We establish some characterizations of this property. In the first one, we define fractional spaces that contain the solution, and we extend it continuously to the natural s...
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| Veröffentlicht in: | Complex analysis and operator theory 2023-04, Vol.17 (3), Article 42 |
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| container_title | Complex analysis and operator theory |
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| creator | Poblete, Felipe Poblete, Verónica Pozo, Juan C. |
| description | In this paper we study a mild wellposedness notion of a second-order abstract differential equation defined in the whole line. We establish some characterizations of this property. In the first one, we define fractional spaces that contain the solution, and we extend it continuously to the natural solution space. The second one is obtained by means of Fourier multipliers over weighted Sobolev spaces on the real line. Further, using an operator-valued version of Miklhin Fourier multipliers theorem, we exhibit some examples of operators for which the mild wellposedness is satisfied. Our results extend some previous results about abstract second order evolution equations. |
| doi_str_mv | 10.1007/s11785-023-01345-9 |
| format | Article |
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| subjects | Analysis Differential equations Evolution Mathematical analysis Mathematics Mathematics and Statistics Multipliers Operator Theory Operators (mathematics) Sobolev space Solution space Spectral Theory and Operators in Mathematical Physics |
| title | Wellposedness of Second Order Evolution Equations |
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