Showing papers in "Journal of Differential Equations in 1992"

TL;DR: In this article, it was shown that if the initial data u(·, 0) has values in both domains of attraction of the potential, then an interface will develop in a short time O(e 2 ¦ ln e¦).

TL;DR: In this paper, it was shown that the discrete Nagumo equation n = d(un −1 +2un + n + 1)+f(un), n eZ has a traveling wave solution for sufficiently strong coupling d.

TL;DR: In this paper, the nonlinear scattering and stability results of Soffer and Weinstein (Comm. Math. Phys. (1990) ) are extended to the case of anisotropic potentials and data.

TL;DR: In this article, the authors considered a system x = (A + eQ(t))x in Rd is considered, where A is a constant matrix and Q a quasiperiodic analytic matrix with r basic frequencies.

TL;DR: Theorem 3 in this article is a generalization of Gard's lemma and guarantees the existence of functions which satisfy the conditions of Theorems 2 and 3 in this paper, respectively.

TL;DR: In this article, the existence of solutions for RN via an inversion to a dual variational problem was proved via an inverse to a variational variational inversion of the problem.

TL;DR: In this paper, the authors prove the global existence, uniqueness, and continuous dependence on initial data for discontinuous solutions of the Navier-Stokes equations for nonisentropic, compressible flow in one space dimension.

TL;DR: In this paper, the authors proved the existence of infinitely many harmonic and subharmonic solutions for the second order scalar nonlinear Duffing's equation x ∆ + g (x ) = p ( t, x, x ) where g and p are continuous functions with p bounded and periodic in the first variable and g satisfying the assumption g(x) sign (x) → + ∞.

TL;DR: In this paper, it is shown that if v is a positive solution of v then any solution becomes unbounded in finite time. But this is not the case for m f 1.

TL;DR: For the semilinear heat equation ut = Δu + eu in a convex domain Ω ⊂ R n, given any b ϵ Ω, the existence of solutions which blow up in finite time exactly at b and whose final profile has the form u(T, x) ≈ −2 ln −x − b¦ + ln ¦x −b¦+ ln ǫ ln n ¦ ln x − b ¦ −ǫ + l n ǵ −ǵ +

TL;DR: In this article, the nonlinear term f is assumed to satisfy the following conditions: (F.l)-(F.2) f(t+l,x,U)=f(t, x,U)for all tE[W, XE[O, L] and UER.

TL;DR: In this paper, the S 1 -degree and bifrucation theory are applied to provide a purely topological argument of a global Hopf bifurcation theory for functional differential equations of mixed type.

TL;DR: In this paper, sufficient conditions for nonexplosion, boundedness, and ergodicity of solutions of a class of semilinear stochastic equations are given, based on a new regularity theorem for solutions of the linear problem.

TL;DR: In this paper, the problem of finding solutions in large differential algebras of generalized functions is addressed, where all differentiations and nonlinear operations involved can be performed unrestrictedly.

TL;DR: In this paper, the authors derived uniform decay rates for the total energy of the solutions to the Euler-Bernoulli equations wherein energy dissipation occurs on the boundary, and proved that the boundary feedback is acting through the moments only.

TL;DR: It is well known that there exist choices of u0 for which the corresponding solutions tend to zero as t -+ cc and other choices for which their solutions blow up in finite time as mentioned in this paper.

TL;DR: For general dissipative evolutionary systems described by semilinear parabolic equations with principal differential operator being sectorial and having compact resolvent, there exists an inertial manifold provided that certain gap conditions hold as discussed by the authors.

TL;DR: In this article, the authors examined the asymptotic behavior at infinity of solutions of some semilinear elliptic equations and considered both radial and non-radial situations.

TL;DR: In this paper, the existence of transversal homoclinic orbits in the circular restricted three-body problem for all but some finite number of values of the mass ratio of the two primaries was shown.

TL;DR: In this paper, it was shown that sufficiently small perturbations of the initial data yield another global solution with the same type of asymptotic behavior, for small and nearly neutral initial data.

TL;DR: In this article, it was shown that for a special class of nonlinear Klein-Gordon equations in two space dimensions, for small initial data, the equation ∂ tt u − Δu + u = u 2 has a global solution.

TL;DR: Stability conditions for periodic (spiral) solutions of homogeneous systems in the non-autonomous and the autonomous case are derived in this article, as well as a concept of Lyapunov functions and a Bendixson criterion.

TL;DR: In this article, it was shown that spontaneous symmetry breaking may also give rise to more complex dynamical behavior, in particular to heteroclinic cycles, and a simple example of their constructions (for the particular choices of groups G = SO (3), H = SO(2), and K = T, described below) in order to illustrate these general ideas.

TL;DR: In this article, a general method is presented to construct sequences of manifolds providing better and better approximations to the attractor, where the concept of variete inertielle approximative intervient dans l'etude du comportement for les grands temps des equations.