The property of unique continuation for second order evolution PDEs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866917613036109824 |
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| author | Choulli, Mourad |
| author_facet | Choulli, Mourad |
| contents | We present a simple and self-contained approach to establish the unique continuation property for some classical evolution equations of second order in a cylindrical domain. We namely discuss this property for wave, parabolic and Schödinger operators with time-independent principal part. Our method is builds on two-parameter Carleman inequalities combined with unique continuation across a pseudo-convex hypersurface with respect to the space variable. The most results we demonstrate in this work are more or less classical. Some of them are not stated exactly as in their original form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_08475 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The property of unique continuation for second order evolution PDEs Choulli, Mourad Analysis of PDEs 35A23, 35J15, 35K10, 35L10 We present a simple and self-contained approach to establish the unique continuation property for some classical evolution equations of second order in a cylindrical domain. We namely discuss this property for wave, parabolic and Schödinger operators with time-independent principal part. Our method is builds on two-parameter Carleman inequalities combined with unique continuation across a pseudo-convex hypersurface with respect to the space variable. The most results we demonstrate in this work are more or less classical. Some of them are not stated exactly as in their original form. |
| title | The property of unique continuation for second order evolution PDEs |
| topic | Analysis of PDEs 35A23, 35J15, 35K10, 35L10 |
| url | https://arxiv.org/abs/2005.08475 |