Blowup behaviour for the nonlinear Klein–Gordon equation
نویسندگان
چکیده
منابع مشابه
Blowup for a Time - Oscillating Nonlinear Heat Equation
In this paper, we study a nonlinear heat equation with a periodic timeoscillating term in factor of the nonlinearity. In particular, we give examples showing how the behavior of the solution can drastically change according to both the frequency of the oscillating factor and the size of the initial value.
متن کاملRefined blowup criteria and nonsymmetric blowup of an aggregation equation
We consider an aggregation equation in Rd, d ≥ 2 with fractional dissipation: ut +∇ · (u∇K ∗ u) = −νΛγu, where ν ≥ 0, 0 < γ < 1 and K(x) = e−|x|. We prove a refined blowup criteria by which the global existence of solutions is controlled by its Lx norm, for any d d−1 ≤ q ≤ ∞. We prove for a general class of nonsymmetric initial data the finite time blowup of the corresponding solutions. The arg...
متن کاملSharp global existence condition and instability by blowup for an inhomogeneous L critical nonlinear Schrödinger equation
An inhomogeneous nonlinear Schrödinger equation is considered, which is invariant under L scaling. The sharp condition for global existence of H solutions is established, involving the L norm of the ground state of the stationary equation. Strong instability of standing waves is proved by constructing self-similar solutions blowing up in finite time.
متن کاملAsymptotics of blowup solutions for the aggregation equation
We consider the asymptotic behavior of radially symmetric solutions of the aggregation equation ut = ∇ · (u∇K ∗ u) in R , for homogeneous potentials K = |x| , γ > 0. For γ > 2, the aggregation happens in infinite time and exhibits a concentration of mass along a collapsing δ-ring. We develop an asymptotic theory for the approach to this singular solution. For γ < 2, the solution blows up in fin...
متن کاملBlowup for the Heat Equation with a Noise Term
In this paper we study blowup of the equation u t = u xx + u _ W tx , where _ W tx is a two-dimensional white noise eld and where Dirichlet boundary conditions are enforced. It is known that if < 3=2, then the solution exists for all time; in this paper we show that if is much larger than 3=2, then the solution blows up in nite time with positive probability. We prove this by considering how pe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2013
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-013-0960-z