Results 21 to 30 of about 74 (70)
Blowup of solutions of a nonlinear wave equation
Journal of Applied Mathematics, Volume 2, Issue 2, Page 105-108, 2002., 2002 We establish a blowup result to an initial boundary value problem for the nonlinear wave equation utt − M(‖B1/2u‖ 2) Bu + kut = |u| p−2, x ∈ Ω, t > 0.
Abbes Benaissa, Salim A. Messaoudi
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Spatial decay estimates for a class of nonlinear damped hyperbolic equations
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 1, Page 17-26, 2001., 2001 This paper is concerned with investigating the spatial decay estimates for a class of nonlinear damped hyperbolic equations. In addition, we compare the solutions of two‐dimensional wave equations with different damped coefficients and establish an explicit inequality which displays continuous dependence on this coefficient.
F. Tahamtani, K. Mosaleheh, K. Seddighi
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On the existence of solutions of strongly damped nonlinear wave equations
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 6, Page 369-382, 2000., 2000 We investigate the existence and uniqueness of solutions of the following equation of hyperbolic type with a strong dissipation: utt(t,x)−(α+β(∫Ω|∇u(t,y)|2dy)γ)Δu(t,x) −λΔut(t,x)+μ|u(t,x)|q−1u(t,x)=00, x∈Ω,t≥ u(0,x)=u0(x), ut(0,x)=u1(x), x∈Ω, u|∂Ω=0 , where q > 1, λ > 0, μ ∈ ℝ, α, β ≥ 0, α + β > 0, and Δ is the Laplacian in ℝN.
Jong Yeoul Park, Jeong Ja Bae
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International Journal of Stochastic Analysis, Volume 12, Issue 2, Page 179-190, 1999., 1998 The aim of the paper is to prove two theorems on the existence of solutions to a nonlocal multivalued Darboux problem. The first theorem concerns the case when the orientor field is convex valued. The second theorem concerns the case when the orientor field is nonconvex valued.
Ludwik Byszewski +1 more
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Exponential decay of the viscoelastic wave equation of Kirchhoff type with a nonlocal dissipation
, 2020 The following viscoelastic wave equation of Kirchhoff type with non- linear and nonlocal damping utt − ψ (I I2\ 2 ∆u − α∆ut t + g(t − τ )∆u(τ )dτ + M 0 (I∇uI2\ u = f (u), where M (r) is a C1([0, ∞)) -function satisfying M (r) ≥ m1 > 0 for r ≥ 0, is ...
MELLAH, Mohamed, HAKEM, Ali
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International Journal of Stochastic Analysis, Volume 3, Issue 3, Page 163-168, 1990., 1990 The aim of the paper is to give two theorems about existence and uniqueness of continuous solutions for hyperbolic nonlinear differential problems with nonlocal conditions in bounded and unbounded domains. The results obtained in this paper can be applied in the theory of elasticity with better effect than analogous known results with classical initial
L. Byszewski
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Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations
International Journal of Mathematics and Mathematical Sciences, Volume 12, Issue 1, Page 137-143, 1989., 1989 The decomposition method is applied to examples of hyperbolic, parabolic, and elliptic partial differential equations without use of linearizatlon techniques. We consider first a nonlinear dissipative wave equation; second, a nonlinear equation modeling convectlon‐diffusion processes; and finally, an elliptic partial differential equation.
G. Adomian
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On a nonolinear wave equation in unbounded domains
International Journal of Mathematics and Mathematical Sciences, Volume 11, Issue 2, Page 335-342, 1988., 1988 We study existence and uniqeness of the nonlinear wave equation in unbounded domains. The above model describes nonlinear wave phenomenon in non‐homogeneous media. Our techniques ivolve fixed point arguments combined with the energy method.
Carlos Frederico Vasconcellos
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Decay of solutions of a system of nonlinear Klein‐Gordon equations
International Journal of Mathematics and Mathematical Sciences, Volume 9, Issue 3, Page 471-483, 1986., 1986 We study the asymptotic behavior in time of the solutions of a system of nonlinear Klein‐Gordon equations. We have two basic results: First, in the L∞(ℝ3) norm, solutions decay like 0(t−3/2) as t → +∞ provided the initial data are sufficiently small. Finally we prove that finite energy solutions of such a system decay in local energy norm as t → +∞.
José Ferreira, Gustavo Perla Menzala
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Journal of Function Spaces, Volume 2024, Issue 1, 2024.In this work, we deal with a fourth‐order parabolic equation with variable exponent logarithmic nonlinearity. We obtain the global existence and blowup solutions using the energy functional and potential well method.
Gülistan Butakın +3 more
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