Decadimento uniforme per equazioni integro-differenziali lineari di Volterra
This talk is devoted to some recent results concerning the exponential and the polynomial decays of the energy associated with a linear Volterra integro-differential equation of hyperbolic type in a Hilbert space, which is an abstract version of the equation describing the motion of a linearly visco...
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| Format: | Article |
| Language: | English |
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University of Bologna
2011-12-01
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| Series: | Bruno Pini Mathematical Analysis Seminar |
| Online Access: | http://mathematicalanalysis.unibo.it/article/view/2669 |
| _version_ | 1818235865144492032 |
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| author | Stefania Gatti |
| author_facet | Stefania Gatti |
| author_sort | Stefania Gatti |
| collection | DOAJ |
| description | This talk is devoted to some recent results concerning the exponential and the polynomial decays of the energy associated with a linear Volterra integro-differential equation of hyperbolic type in a Hilbert space, which is an abstract version of the equation describing the motion of a linearly viscoelastic solid occupying a (bounded) volume at rest.We provide sufficient conditions for the decay to hold, without invoking differential inequalities involving the convolution kernel. A similar analysis is carried on in the whole N-dimensional real space, although both the polynomial and the exponential decay of the memory kernel lead to a polynomial decay of the energy, with a rate influenced by the space dimension N. These results are contained in two joint papers with Monica Conti and Vittorino Pata (Politecnico di Milano). |
| first_indexed | 2024-12-12T12:00:45Z |
| format | Article |
| id | doaj.art-96123344cdef4a1ba9bc49059ee149d9 |
| institution | Directory Open Access Journal |
| issn | 2240-2829 |
| language | English |
| last_indexed | 2024-12-12T12:00:45Z |
| publishDate | 2011-12-01 |
| publisher | University of Bologna |
| record_format | Article |
| series | Bruno Pini Mathematical Analysis Seminar |
| spelling | doaj.art-96123344cdef4a1ba9bc49059ee149d92022-12-22T00:25:07ZengUniversity of BolognaBruno Pini Mathematical Analysis Seminar2240-28292011-12-01212482Decadimento uniforme per equazioni integro-differenziali lineari di VolterraStefania Gatti0Università di Modena - Reggio EmiliaThis talk is devoted to some recent results concerning the exponential and the polynomial decays of the energy associated with a linear Volterra integro-differential equation of hyperbolic type in a Hilbert space, which is an abstract version of the equation describing the motion of a linearly viscoelastic solid occupying a (bounded) volume at rest.We provide sufficient conditions for the decay to hold, without invoking differential inequalities involving the convolution kernel. A similar analysis is carried on in the whole N-dimensional real space, although both the polynomial and the exponential decay of the memory kernel lead to a polynomial decay of the energy, with a rate influenced by the space dimension N. These results are contained in two joint papers with Monica Conti and Vittorino Pata (Politecnico di Milano).http://mathematicalanalysis.unibo.it/article/view/2669 |
| spellingShingle | Stefania Gatti Decadimento uniforme per equazioni integro-differenziali lineari di Volterra Bruno Pini Mathematical Analysis Seminar |
| title | Decadimento uniforme per equazioni integro-differenziali lineari di Volterra |
| title_full | Decadimento uniforme per equazioni integro-differenziali lineari di Volterra |
| title_fullStr | Decadimento uniforme per equazioni integro-differenziali lineari di Volterra |
| title_full_unstemmed | Decadimento uniforme per equazioni integro-differenziali lineari di Volterra |
| title_short | Decadimento uniforme per equazioni integro-differenziali lineari di Volterra |
| title_sort | decadimento uniforme per equazioni integro differenziali lineari di volterra |
| url | http://mathematicalanalysis.unibo.it/article/view/2669 |
| work_keys_str_mv | AT stefaniagatti decadimentouniformeperequazioniintegrodifferenzialilinearidivolterra |