On Mixed Problems for Quasilinear Second-Order Systems
The paper is devoted to the study of initial-boundary value problems for quasilinear second-order systems. Existence and uniqueness of the solution in the space 𝐻𝑠(Ω×[0,𝑇]), with 𝑠>𝑑/2+3, is proved in the case where Ω is a half-space of ℜ𝑑. The proof of the main theorem relies on two prelimina...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2010/464251 |
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| _version_ | 1850104393803759616 |
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| author | Rita Cavazzoni |
| author_facet | Rita Cavazzoni |
| author_sort | Rita Cavazzoni |
| collection | DOAJ |
| description | The paper is devoted to the study of initial-boundary value problems for quasilinear second-order systems. Existence and uniqueness of the solution in the space 𝐻𝑠(Ω×[0,𝑇]), with 𝑠>𝑑/2+3, is proved in the case where Ω is a half-space of ℜ𝑑. The proof of the main theorem relies on two preliminary results: existence of the solution to mixed problems for linear second-order systems with smooth coefficients, and existence of the solution to initial-boundary value problems for linear second-order operators whose coefficients depend on the variables 𝑥 and 𝑡 through a function 𝑣∈𝐻𝑠(ℜ𝑑+1). By means of the results proved for linear operators, the well posedness of the mixed problem for the quasi-linear system is established by studying the convergence of a suitable iteration scheme. |
| format | Article |
| id | doaj-art-47688a7eda8f442e9698a8b836694efd |
| institution | DOAJ |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-47688a7eda8f442e9698a8b836694efd2025-08-20T02:39:21ZengWileyInternational Journal of Differential Equations1687-96431687-96512010-01-01201010.1155/2010/464251464251On Mixed Problems for Quasilinear Second-Order SystemsRita Cavazzoni0via Millaures, 12–10146 Turin, ItalyThe paper is devoted to the study of initial-boundary value problems for quasilinear second-order systems. Existence and uniqueness of the solution in the space 𝐻𝑠(Ω×[0,𝑇]), with 𝑠>𝑑/2+3, is proved in the case where Ω is a half-space of ℜ𝑑. The proof of the main theorem relies on two preliminary results: existence of the solution to mixed problems for linear second-order systems with smooth coefficients, and existence of the solution to initial-boundary value problems for linear second-order operators whose coefficients depend on the variables 𝑥 and 𝑡 through a function 𝑣∈𝐻𝑠(ℜ𝑑+1). By means of the results proved for linear operators, the well posedness of the mixed problem for the quasi-linear system is established by studying the convergence of a suitable iteration scheme.http://dx.doi.org/10.1155/2010/464251 |
| spellingShingle | Rita Cavazzoni On Mixed Problems for Quasilinear Second-Order Systems International Journal of Differential Equations |
| title | On Mixed Problems for Quasilinear Second-Order Systems |
| title_full | On Mixed Problems for Quasilinear Second-Order Systems |
| title_fullStr | On Mixed Problems for Quasilinear Second-Order Systems |
| title_full_unstemmed | On Mixed Problems for Quasilinear Second-Order Systems |
| title_short | On Mixed Problems for Quasilinear Second-Order Systems |
| title_sort | on mixed problems for quasilinear second order systems |
| url | http://dx.doi.org/10.1155/2010/464251 |
| work_keys_str_mv | AT ritacavazzoni onmixedproblemsforquasilinearsecondordersystems |