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On asymptotic behavior of solution to a nonlinear wave equation with space-time speed of propagation and damping terms
In this paper, we consider the asymptotic behavior of solution to the nonlinear damped wave equationutt − div¡a(t, x)∇u¢+ b(t, x)ut = −|u|p−1u t ∈ [0, ∞), x ∈ Rn u(0, x) = u0(x), ut(0, x) = u1(x) x ∈ Rn with space-time speed of propagation and damping potential. We obtained L2 decay estimates via th...
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2021-12
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| LEADER | 00000njm a2000000a 4500 | ||
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| 001 | oai:repository.ui.edu.ng:123456789/8114 | ||
| 042 | |a dc | ||
| 720 | |a Ogbiyele, P. A. |e author | ||
| 720 | |a Arawomo, P. O. |e author | ||
| 260 | |c 2021-12 | ||
| 520 | |a In this paper, we consider the asymptotic behavior of solution to the nonlinear damped wave equationutt − div¡a(t, x)∇u¢+ b(t, x)ut = −|u|p−1u t ∈ [0, ∞), x ∈ Rn u(0, x) = u0(x), ut(0, x) = u1(x) x ∈ Rn with space-time speed of propagation and damping potential. We obtained L2 decay estimates via the weighted energy method and under certain suitable assumptions on the functions a(t, x) and b(t, x). The technique follows that of Lin et al.[8] with modification to the region of consideration in Rn. These decay result extends the results in the literature. | ||
| 024 | 8 | |a ui_art_ogbiyele_on_2021 | |
| 024 | 8 | |a Proyecciones Journal of Mathematics 40(6), pp. 1615-1639 | |
| 024 | 8 | |a http://ir.library.ui.edu.ng/handle/123456789/8114 | |
| 653 | |a Space-time speed of propagation | ||
| 653 | |a Space-time dependent damping | ||
| 653 | |a Asymptotic behavior | ||
| 653 | |a Weighted energy method | ||
| 245 | 0 | 0 | |a On asymptotic behavior of solution to a nonlinear wave equation with space-time speed of propagation and damping terms |