Blow up Near Higher Modes of Nonlinear Wave Equations
نویسندگان
چکیده
منابع مشابه
Blow-Up for Nonlinear Wave Equations describing Boson Stars
We consider the nonlinear wave equation i∂tu = √ −∆+m2u− (|x| ∗ |u|)u on R modelling the dynamics of (pseudo-relativistic) boson stars. For spherically symmetric initial data, u0(x) ∈ C∞ c (R), with negative energy, we prove blow-up of u(t, x) inH-norm within a finite time. Physically, this phenomenon describes the onset of “gravitational collapse” of a boson star. We also study blow-up in exte...
متن کاملBLOW-UP AND NONGLOBAL SOLUTION FOR A FAMILY OF NONLINEAR HIGHER-ORDER EVOLUTION PROBLEM
In this paper we consider a kind of higher-order evolution equation as^{kt^{k} + ^{k&minus1}u/t^{k&minus1} +• • •+ut &minus{delta}u= f (u, {delta}u,x). For this equation, we investigate nonglobal solution, blow-up in finite time and instantaneous blow-up under some assumption on k, f and initial data. In this paper we employ the Test function method, the eneralized convexity method an...
متن کاملBlow-up in Nonlinear Heat Equations
In this paper we study the blowup problem of nonlinear heat equations. Our result show that for a certain family of initial conditions the solution will blowup in finite time, the blowup parameters satisfy some dynamics which are asymptotic stable, moreover we provide the remainder estimates. Compare to the previous works our approach is analogous to one used in bifurcation theory and our techn...
متن کاملBlow-up of solutions of nonlinear wave equations in three space dimensions.
Solutions u(x, t) of the inequality squareu >/= A|u|(p) for x epsilon R(3), t >/= 0 are considered, where square is the d'Alembertian, and A,p are constants with A > 0, 1 < p < 1 + radical2. It is shown that the support of u is compact and contained in the cone 0 </= t </= t(0) -|x - x(0)|, if the "initial data" u(x, 0), u(t)(x, 0) have their support in the ball|x - x(0)| </= t(0). In particula...
متن کاملBlow up of Solutions for a System of Nonlinear Higher-order Kirchhoff-type Equations
In this work, we consider the initial boundary value problem for the Kirchhoff-type equations with damping and source terms utt +M (∫ Ω ∣∣∣(−△)m2 u∣∣∣2 dx) (−△) u+ |ut| ut = f1 (u, v) , vtt +M (∫ Ω ∣∣∣(−△)m2 v∣∣∣2 dx) (−△) v + |vt| vt = f2 (u, v) in a bounded domain. We prove the blow up of the solution with positive initial energy by using the technique of [26] with a modification in th...
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: Transactions of the American Mathematical Society
سال: 1986
ISSN: 0002-9947
DOI: 10.2307/2000576