Global solutions and finite time blow up for damped semilinear wave equations
نویسنده
چکیده
A class of damped wave equations with superlinear source term is considered. It is shown that every global solution is uniformly bounded in the natural phase space. Global existence of solutions with initial data in the potential well is obtained. Finally, not only finite time blow up for solutions starting in the unstable set is proved, but also high energy initial data for which the solution blows up are constructed.
منابع مشابه
Existence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation
In this paper, we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation. Moreover, the finite-time blow-up of the solution for the equation is investigated by the concavity method.
متن کاملFinite Time Blow-up and Global Solutions for Semilinear Parabolic Equations with Initial Data at High Energy Level
For a class of semilinear parabolic equations on a bounded domain Ω, we analyze the behavior of the solutions when the initial data varies in the phase space H 0 (Ω). We obtain both global solutions and finite time blow-up solutions. Our main tools are the comparison principle and variational methods. Particular attention is paid to initial data at high energy level; to this end, a basic new id...
متن کاملFinite-time Blow-up and Global Solutions for Some Nonlinear Parabolic Equations
For a class of semilinear parabolic equations, we prove both global existence and finite-time blow-up depending on the initial datum. The proofs involve tools from the potential-well theory, from the criticalpoint theory, and from classical comparison principles.
متن کاملFinite Time Blow up for Critical Wave Equations in High Dimensions: Completion of the Proof of Strauss Conjecture
We prove that solutions to the critical wave equation (1.1) with dimension n ≥ 4 can not be global if the initial values are positive somewhere and nonnegative. This completes the solution to the famous conjecture about semilinear wave equations of the form ∆u− ∂ t u + |u| = 0. The rest of the cases, the lower dimensional case n ≤ 3, and the sub or super critical cases were settled many years e...
متن کاملClassification of Connecting Solutions of Semilinear Parabolic Equations
Abstract. For a given semilinear parabolic equation with polynomial nonlinearity, many solutions blow up in finite time. For a certain large class of these equations, we show that some of the solutions which do not blow up actually tend to equilibria. The characterizing property of such solutions is a finite energy constraint, which comes about from the fact that this class of equations can be ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004