On the global solvability of solutions to a quasilinear wave equation with localized damping and source terms
We prove existence and uniform stability of strong solutions to a quasilinear wave equation with a locally distributed nonlinear dissipation with source term of power nonlinearity of the type u″−M(∫Ω|∇u|2dx)Δu+a(x)g(u′)+f(u)=0, in Ω×]0,+∞[, u=0, on Γ×]0,+∞[,u(x,0)=u0(x),u′(x,0)=u1(x), in Ω....
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2005-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/JAM.2005.219 |
| _version_ | 1827001816431198208 |
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| author | E. Cabanillas Lapa Z. Huaringa Segura F. Leon Barboza |
| author_facet | E. Cabanillas Lapa Z. Huaringa Segura F. Leon Barboza |
| author_sort | E. Cabanillas Lapa |
| collection | DOAJ |
| description | We prove existence and uniform stability of strong solutions to a
quasilinear wave equation with a locally distributed nonlinear dissipation with source term of power nonlinearity of
the type u″−M(∫Ω|∇u|2dx)Δu+a(x)g(u′)+f(u)=0, in Ω×]0,+∞[, u=0, on Γ×]0,+∞[,u(x,0)=u0(x),u′(x,0)=u1(x), in Ω. |
| first_indexed | 2024-04-12T13:55:55Z |
| format | Article |
| id | doaj.art-7b1467d689894e38a1cfab2568ca7029 |
| institution | Directory Open Access Journal |
| issn | 1110-757X 1687-0042 |
| language | English |
| last_indexed | 2025-02-18T11:04:00Z |
| publishDate | 2005-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj.art-7b1467d689894e38a1cfab2568ca70292024-11-02T05:24:23ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422005-01-012005321923310.1155/JAM.2005.219On the global solvability of solutions to a quasilinear wave equation with localized damping and source termsE. Cabanillas Lapa0Z. Huaringa Segura1F. Leon Barboza2Instituto de Investigación, Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Lima, PeruInstituto de Investigación, Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Lima, PeruInstituto de Investigación, Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Lima, PeruWe prove existence and uniform stability of strong solutions to a quasilinear wave equation with a locally distributed nonlinear dissipation with source term of power nonlinearity of the type u″−M(∫Ω|∇u|2dx)Δu+a(x)g(u′)+f(u)=0, in Ω×]0,+∞[, u=0, on Γ×]0,+∞[,u(x,0)=u0(x),u′(x,0)=u1(x), in Ω.http://dx.doi.org/10.1155/JAM.2005.219 |
| spellingShingle | E. Cabanillas Lapa Z. Huaringa Segura F. Leon Barboza On the global solvability of solutions to a quasilinear wave equation with localized damping and source terms Journal of Applied Mathematics |
| title | On the global solvability of solutions to a quasilinear
wave equation with localized damping and source terms |
| title_full | On the global solvability of solutions to a quasilinear
wave equation with localized damping and source terms |
| title_fullStr | On the global solvability of solutions to a quasilinear
wave equation with localized damping and source terms |
| title_full_unstemmed | On the global solvability of solutions to a quasilinear
wave equation with localized damping and source terms |
| title_short | On the global solvability of solutions to a quasilinear
wave equation with localized damping and source terms |
| title_sort | on the global solvability of solutions to a quasilinear wave equation with localized damping and source terms |
| url | http://dx.doi.org/10.1155/JAM.2005.219 |
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