Controllability of strongly degenerate parabolic problems with strongly singular potentials
We prove a null controllability result for a parabolic Dirichlet problem with non smooth coefficients in presence of strongly singular potentials and a coefficient degenerating at an interior point. We cover the case of weights falling out the class of Muckenhoupt functions, so that no Hardy-type in...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2018-06-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6658 |
| _version_ | 1797830520435900416 |
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| author | Genni Fragnelli Dimitri Mugnai |
| author_facet | Genni Fragnelli Dimitri Mugnai |
| author_sort | Genni Fragnelli |
| collection | DOAJ |
| description | We prove a null controllability result for a parabolic Dirichlet problem with non smooth coefficients in presence of strongly singular potentials and a coefficient degenerating at an interior point. We cover the case of weights falling out the class of Muckenhoupt functions, so that no Hardy-type inequality is available; for instance, we can consider Coulomb-type potentials. However, through a cut-off function method, we recover the desired controllability result. |
| first_indexed | 2024-04-09T13:38:28Z |
| format | Article |
| id | doaj.art-8643de46d1414633859808668c85fca9 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:28Z |
| publishDate | 2018-06-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-8643de46d1414633859808668c85fca92023-05-09T07:53:08ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752018-06-0120185011110.14232/ejqtde.2018.1.506658Controllability of strongly degenerate parabolic problems with strongly singular potentialsGenni Fragnelli0Dimitri Mugnai1University of Bari, Bari, ItalyDepartment of Ecology and Biology, University of Tuscia, Viterbo, ItalyWe prove a null controllability result for a parabolic Dirichlet problem with non smooth coefficients in presence of strongly singular potentials and a coefficient degenerating at an interior point. We cover the case of weights falling out the class of Muckenhoupt functions, so that no Hardy-type inequality is available; for instance, we can consider Coulomb-type potentials. However, through a cut-off function method, we recover the desired controllability result.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6658strong degeneracystrong singularitynon smooth coefficientscoulomb potentialnull controllabilitycut-off functions |
| spellingShingle | Genni Fragnelli Dimitri Mugnai Controllability of strongly degenerate parabolic problems with strongly singular potentials Electronic Journal of Qualitative Theory of Differential Equations strong degeneracy strong singularity non smooth coefficients coulomb potential null controllability cut-off functions |
| title | Controllability of strongly degenerate parabolic problems with strongly singular potentials |
| title_full | Controllability of strongly degenerate parabolic problems with strongly singular potentials |
| title_fullStr | Controllability of strongly degenerate parabolic problems with strongly singular potentials |
| title_full_unstemmed | Controllability of strongly degenerate parabolic problems with strongly singular potentials |
| title_short | Controllability of strongly degenerate parabolic problems with strongly singular potentials |
| title_sort | controllability of strongly degenerate parabolic problems with strongly singular potentials |
| topic | strong degeneracy strong singularity non smooth coefficients coulomb potential null controllability cut-off functions |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6658 |
| work_keys_str_mv | AT gennifragnelli controllabilityofstronglydegenerateparabolicproblemswithstronglysingularpotentials AT dimitrimugnai controllabilityofstronglydegenerateparabolicproblemswithstronglysingularpotentials |