[PDF] Top 20 Existence and Asymptotic Behavior of Global Solutions for a Class of Nonlinear Higher Order Wave Equation

... the existence and uniqueness, as well as decay estimates, of global solutions and blow up of solutions for the initial boundary value problem and Cauchy problem of ...with wave ... See full document

... the existence of global solutions under the condition  < p ≤ ...of solutions for sufficiently large initial ...a global solution for sufficiently small initial ...the global ... See full document

... differential equation is associated with problems that are described by the development of long time ...the global properties of the solutions have been well studied, researchers in various fields ... See full document

... The global attractor and their Hausdorff and Fractal dimensions estimation for the higher-order nonlinear Kirchhoff-type equation ... See full document

... the behavior of solutions of a given differential equation and does not seek explicit ...then, asymptotic and oscillatory properties of solutions to different equations, functional ... See full document

... the existence and uniqueness of energy solutions in the case where the growth exponent of the non-linearity φ is less than 6 and f may have arbitrary polynomial growth ...the existence of a ... See full document

... the global existence of solution for ...the existence of solutions to nonlinear wave ...the wave equation u tt − Δu gu t 0 in Ω × R , where ... See full document

... This problem has its origin in the mathematical description of viscoelastic materials. It is well known that viscoelastic materials exhibit natural damping, which is due to the special property of these materials to ... See full document

... where q : Ω → R + is a bounded function. Under some assumptions, he showed the solution of (1.9) decays exponentially if g behaves like a linear function, whereas the decay is polynomially otherwise. For more decay ... See full document

... a class of fourth-order wave equations in an n-dimensional ...of solutions to the corresponding linear equation, a solution space is ...the global existence and optimal ... See full document

... a nonlinear damping ...the nonlinear case (p > 1). They showed that solutions with negative initial energy blow up in finite ...the nonlinear damping and the solution has positive initial ... See full document

... of solutions for a class of sixth order 1-D nonlinear wave equations at high initial energy ...certain solutions with arbitrarily positive initial energy exist ... See full document

... minimal wave speed, spreading speed is also an important threshold, which may equal to the minimal wave speed of traveling wave ...the asymptotic spreading of each species remains ... See full document

... the existence of weak solutions by using Faedo-Galerkin approximations to the IBVP of ...strong solutions and the expo- nential stability of solutions to ... See full document

... 1) Equation (14) has a solution of type (D) if and only if σ ≥ − − α 1 (Theorem ...2) Equation (14) has a solution of type (AC) if and only if σ < − − α 1 (Theorem ...3) Equation (14) has a ... See full document

... Houari [15]. Also, he showed that the local solution obtained in [2] is global and decay of solutions [14]. Recently, Han and Wang [4] obtained the local existence, global existence and ... See full document

... is the discrete version of (1). The model (1) ignores many complicating factors such as those due to age structure, spatial distribution and migration, sexual categories and others. The delayed logistic equation ... See full document

... the wave equation ...damped wave equation with dynamic boundary ...the nonlinear dissipative damping term h(u t ) play a dissipative or ... See full document

... the global existence, decay, and blow up of solutions for a quasilinear hyperbolic ...of solutions and lifespan estimates in three different ranges of the initial ... See full document

... Recently the control of wave equations with time delay effects has become an active area of research. The delay effects often appear in many practical problems and may turn a well-behaved system into a wild one. The ... See full document