<i>L</i><sup>p</sup>-<i>L</i><sup>q</sup>-Well Posedness for the Moore–Gibson–Thompson Equation with Two Temperatures on Cylindrical Domains
We examine the Cauchy problem for a model of linear acoustics, called the Moore–Gibson–Thompson equation, describing a sound propagation in thermo-viscous elastic media with two temperatures on cylindrical domains. For an adequate combination of the parameters of the model we prove <inline-formul...
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MDPI AG
2020-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/10/1748 |
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| author | Carlos Lizama Marina Murillo-Arcila |
| author_facet | Carlos Lizama Marina Murillo-Arcila |
| author_sort | Carlos Lizama |
| collection | DOAJ |
| description | We examine the Cauchy problem for a model of linear acoustics, called the Moore–Gibson–Thompson equation, describing a sound propagation in thermo-viscous elastic media with two temperatures on cylindrical domains. For an adequate combination of the parameters of the model we prove <inline-formula><math display="inline"><semantics><msup><mi>L</mi><mi>p</mi></msup></semantics></math></inline-formula>-<inline-formula><math display="inline"><semantics><msup><mi>L</mi><mi>q</mi></msup></semantics></math></inline-formula>-well-posedness, and we provide maximal regularity estimates which are optimal thanks to the theory of operator-valued Fourier multipliers. |
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| format | Article |
| id | doaj.art-6b8bbd68976745f6abd2431640d5eba3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:42:24Z |
| publishDate | 2020-10-01 |
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| spelling | doaj.art-6b8bbd68976745f6abd2431640d5eba32023-11-20T16:42:55ZengMDPI AGMathematics2227-73902020-10-01810174810.3390/math8101748<i>L</i><sup>p</sup>-<i>L</i><sup>q</sup>-Well Posedness for the Moore–Gibson–Thompson Equation with Two Temperatures on Cylindrical DomainsCarlos Lizama0Marina Murillo-Arcila1Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencias, Universidad de Santiago de Chile, Las Sophoras 173, Estación Central, Santiago 9160000, ChileInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 València, SpainWe examine the Cauchy problem for a model of linear acoustics, called the Moore–Gibson–Thompson equation, describing a sound propagation in thermo-viscous elastic media with two temperatures on cylindrical domains. For an adequate combination of the parameters of the model we prove <inline-formula><math display="inline"><semantics><msup><mi>L</mi><mi>p</mi></msup></semantics></math></inline-formula>-<inline-formula><math display="inline"><semantics><msup><mi>L</mi><mi>q</mi></msup></semantics></math></inline-formula>-well-posedness, and we provide maximal regularity estimates which are optimal thanks to the theory of operator-valued Fourier multipliers.https://www.mdpi.com/2227-7390/8/10/1748well-posednessMoore–Gibson–Thompson equationdegenerate evolution equationsR-boundedness |
| spellingShingle | Carlos Lizama Marina Murillo-Arcila <i>L</i><sup>p</sup>-<i>L</i><sup>q</sup>-Well Posedness for the Moore–Gibson–Thompson Equation with Two Temperatures on Cylindrical Domains Mathematics well-posedness Moore–Gibson–Thompson equation degenerate evolution equations R-boundedness |
| title | <i>L</i><sup>p</sup>-<i>L</i><sup>q</sup>-Well Posedness for the Moore–Gibson–Thompson Equation with Two Temperatures on Cylindrical Domains |
| title_full | <i>L</i><sup>p</sup>-<i>L</i><sup>q</sup>-Well Posedness for the Moore–Gibson–Thompson Equation with Two Temperatures on Cylindrical Domains |
| title_fullStr | <i>L</i><sup>p</sup>-<i>L</i><sup>q</sup>-Well Posedness for the Moore–Gibson–Thompson Equation with Two Temperatures on Cylindrical Domains |
| title_full_unstemmed | <i>L</i><sup>p</sup>-<i>L</i><sup>q</sup>-Well Posedness for the Moore–Gibson–Thompson Equation with Two Temperatures on Cylindrical Domains |
| title_short | <i>L</i><sup>p</sup>-<i>L</i><sup>q</sup>-Well Posedness for the Moore–Gibson–Thompson Equation with Two Temperatures on Cylindrical Domains |
| title_sort | i l i sup p sup i l i sup q sup well posedness for the moore gibson thompson equation with two temperatures on cylindrical domains |
| topic | well-posedness Moore–Gibson–Thompson equation degenerate evolution equations R-boundedness |
| url | https://www.mdpi.com/2227-7390/8/10/1748 |
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