Asymptotic behavior of solutions to quasilinear hyperbolic equations with nonlinear damping

Asymptotic Behavior of Solutions to Quasilinear Hyperbolic Equations with Nonlinear Damping

Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic Equation

(x 1 , . . . , x n ) ∈ Rn and t > 0, k 1 > 0 and k 2 > 0 are constants. The nonlinear termf(u) = O(u1+θ) and θ is a positive integer. Equation (1) is a model in variational form for the neoHookean elastomer rod and describes the motion of a neoHookean elastomer rod with internal damping; for more detailed physical background, we refer to [1]. In [1], the authors have studied a general class of ...

Asymptotic Behavior of Solutions of Nonlinear Functional Differential Equations

Using the properties of almost nonexpansive curves introduced by B. Djafari Rouhani, we study the asymptotic behavior of solutions of nonlinear functional differential equation du(t)/dt + Au(t)+ G(u)(t) f(t), where A is a maximal monotone operator in a nilbert space H,f E LI(0,:H) and G:C([O,c):D(A))LI(O,c:H)is a given mapping.

Asymptotic Behavior of the Solutions of Nonlinear Differential Equations

3. J. S. MacNerney, Stieltjes integrals in linear spaces, Ann. of Math. (2) 61 (1955), 354-367. 4. -, Continuous products in linear spaces, J. Elisha Mitchell Sei. Soc. 71 (1955), 185-200. 5. ■-, Determinants of harmonic matrices, Proc. Amer. Math. Soc. 7 (1956), 1044-1046. 6. F. W. Stallard, Differential systems with interface conditions, Oak Ridge National Laboratory Publication no. 1876 (Phy...

Asymptotic Behavior of Solutions of Nonlinear Difference Equations

The nonlinear difference equation (E) xn+1 − xn = anφn(xσ(n)) + bn, where (an), (bn) are real sequences, φn : −→ , (σ(n)) is a sequence of integers and lim n−→∞ σ(n) =∞, is investigated. Sufficient conditions for the existence of solutions of this equation asymptotically equivalent to the solutions of the equation yn+1 − yn = bn are given. Sufficient conditions under which for every real consta...