GLOBAL SOLUTIONS TO THE NONLINEAR HYPERBOLIC PROBLEM
نویسندگان
چکیده
منابع مشابه
Nonexistence of Global Solutions of a Nonlinear Hyperbolic System
Consider the initial value problem utt = ∆u+ |v|p, vtt = ∆v + |u|q, x ∈ Rn, t > 0, u(x, 0) = f(x), v(x, 0) = h(x), ut(x, 0) = g(x), vt(x, 0) = k(x), with 1 ≤ n ≤ 3 and p, q > 0. We show that there exists a bound B(n) (≤ ∞) such that if 1 < pq < B(n) all nontrivial solutions with compact support blow up in finite time.
متن کاملGlobal solutions to hyperbolic Navier-Stokes equations
We consider a hyperbolicly perturbed Navier-Stokes initial value problem in R, n = 2, 3, arising from using a Cattaneo type relation instead of a Fourier type one in the constitutive equations. The resulting system is a hyperbolic one with quasilinear nonlinearities. The global existence of smooth solutions for small data is proved, and relations to the classical Navier-Stokes systems are discu...
متن کاملOn the Existence or the Absence of Global Solutions of the Cauchy Characteristic Problem for Some Nonlinear Hyperbolic Equations
where g is the given real function on the characteristic conic surface ST : t = |x|, t ≤ T . When considering the case T = +∞ we assume that D∞ : t > |x| and S∞ = ∂D∞ : t = |x|. Note that the questions on the existence or nonexistence of a global solution of the Cauchy problem for semilinear equations of type (1.1) with initial conditions u|t=0 = u0, ∂u/∂t|t=0 = u1 have been considered in [1, 2...
متن کاملStability of Entropy Solutions to the Cauchy Problem for a Class of Nonlinear Hyperbolic-Parabolic Equations
Consider the Cauchy problem for the nonlinear hyperbolic-parabolic equation: (*) ut + 1 2 a · ∇xu = ∆u+ for t > 0, where a is a constant vector and u+ = max{u, 0}. The equation is hyperbolic in the region [u < 0] and parabolic in the region [u > 0]. It is shown that entropy solutions to (*), that grow at most linearly as |x| → ∞, are stable in a weighted L(IR ) space, which implies that the sol...
متن کاملAsymptotic 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 ...
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: Pesquimat
سال: 2014
ISSN: 1609-8439,1560-912X
DOI: 10.15381/pes.v1i2.8643