Browsing by Author "Ogbiyele, P. A."

Now showing 1 - 5 of 5

Blow up for a viscoelastic wave equation with space-time potential in Rn
(2022-07) Ogbiyele, P. A.; Arawomo, P. O.
In this paper, we consider the following wave equation: with space-time dependent potential, where the initial data have compact support. Under suitable assumptions on the nonlinear function f, the relaxation function g and the damping potential b, we obtain blow up results using the perturbed energy method.
Energy decay for a viscoelastic wave equation with space-time potential in Rn
(Elsevier Inc., 2022) Ogbiyele, P. A.; Arawomo, P. O.
In this paper, we consider the following viscoelastic wave equation with space-time dependent potential and where the initial data u0(x), u1(x)have compact support. Under suitable assumptions on the relaxation function g and the potential b, we obtain a more general energy decay result using the perturbed energy method.
Existence and Blow up Time Estimate for a negative initial energy solution of a nonlinear cauchy problem
(Springer Nature B.V., 2020-06) Ogbiyele, P. A.; Arawomo, P. O.
In this paper, we consider nonlinear wave equations with dissipation having the form utt −div_(|∇u|γ−2∇u)+b(t, x)|ut |m−2ut = g(x,u) for (t, x) ∈ [0,∞) × Rn. We obtain existence and blow up results under suitable assumptions on the positive function b(t, x) and the nonlinear function g(x,u). The existence result was obtained using the Galerkin approach while the blow up result was obtained via the perturbed energy method. Our result improves on the perturbed energy technique for unbounded domains.
On asymptotic behavior of solution to a nonlinear wave equation with space-time speed of propagation and damping terms
(2021-12) Ogbiyele, P. A.; Arawomo, P. O.
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.
On blow up of positive initial energy solution of a nonlinear wave equation with nonlinear source and boundary damping terms
(2021-08) Ogbiyele, P. A.; Arawomo, P. O.
In this paper, we consider a nonlinear wave equation having nonlinear source and boundary damping terms and obtain blow up results under certain polynomial growth conditions on y, r, m and p, where the polynomial growth order of the nonlinear functions g and / are p + 1 and to +1 respectively. We obtain the blow up result using the perturbed energy technique.