Showing papers in "Journal of Differential Equations in 1995"

TL;DR: In this article, the authors prove the global existence of weak solutions of Navier-Stokes equations for compressible, isothermal flow in two and three space dimensions when the initial density is close to a constant in L 2 and L ∞, and the initial velocity is small in 2 and bounded in 2 n (in two dimensions the L 2 norms must be weighted slightly).

TL;DR: In this article, the authors considered the problem of normal forms associated with the flow on a finite-dimensional invariant manifold tangent to an invariant space for the infinitesimal generator of the linearized equation at a singularity.

TL;DR: In this article, the authors give apriori estimates for solutions of the prescribed scalar curvature equations for n ≥ 3 and some existence results which are quite natural extensions of previous results of Chang and Yang ([CY2]), Bahri and Coron ([BC2]) for n = 2, 3.

TL;DR: In this paper, a phase space appropriate to the computation of normal forms associated with the flow on a finite-dimensional invariant manifold tangent to invariant spaces for the infinitesimal generator of the linearized equation at a singularity is introduced, and adequate nonresonance conditions for the normal forms are derived.

TL;DR: In this article, the authors introduced the concept of exponential dichotomy for skew-product semi-low in infinite dimensional Banach spaces, which is an extension of the classic concept for evolution operators.

TL;DR: In this article, the question of uniform persistence for functional differential equations was investigated and it was shown that the conditions which guarantee the existence of an interior equilibrium are enough to ensure uniform persistence.

TL;DR: In this paper, a model system of strictly hyperbolic conservation laws which is genuinely nonlinear but for which the Riemann problem has no global solution is studied. And the authors show that approximate solutions which can be constructed by several standard methods converge in a weighted measure space and that the error in the approximation converges to zero.

TL;DR: In this article, isochronous centers of polynomial systems have been studied and a unified proof of the isochronicity of these systems has been given by constructing algebraic linearizing changes of coordinates.

TL;DR: In this paper, the authors prove viability and invariance theorems for systems with dynamics depending on time in a measurable way and having time dependent state constraints: x′(t) ∈ F(t, x(t)), x ∈ P(t).

TL;DR: In this article, the authors prove the global existence of a solution to the Euler-Poisson system, with arbitrarily large data, in a one-dimensional geometry, by deducing the pressure law from an isothermal assumption for the electrons gas.

TL;DR: In this article, the authors studied the existence of travelling wave solutions (t.w.s.) of front type for the Fisher-KPP equation with different assumptions on the non-linear diffusion term D ( u ), where the reactive part g ( u ) is defined on the interval [0, 1].

TL;DR: In this article, the stability of the solitary wave for the Schrodinger equation was analyzed for the case s 2 ≠ 0, and the results of Grillakis et al. [5, 6] do not apply directly.

TL;DR: In this paper, a smoothing effect of a non-linear degenerate parabolic problem, the Vlasov-Poisson-Fokker-Planck system, in three dimensions was studied.

TL;DR: In this article, it was shown that if σ(A) ∩ i R is countable and ƒ: R → E → E is [asymptotically] almost periodic, then every bounded and uniformly continuous solution u to (∗) is almost periodic.

TL;DR: In this paper, the dynamics of the 1-dimensional Cahn-Hilliard equation u t = (−ϵ 2 u xx + W ′( u )) xx in a finite interval in a neighborhood of an equilibrium with N + 1 transition layers, where ϵ is a small parameter and W is a double well energy density function with equal minima.

TL;DR: In this article, a bifurcation function, H, is constructed between two finite dimensional spaces where the zeros of H correspond to homoclinic solutions at nonzero parameter values.

TL;DR: In this article, the roughness theorem for a class of (h,k)-dichotomies of linear systems of differential equations was shown to generalize the property of roughness of ordinary dichotomies under integrable perturbations.

TL;DR: In this article, a complete classification of the evolution equations ∂ u /∂ t = F ( u, ∆ u / ∆ t = f ( u, ∀ u/∆ t ) for pseudo-spherical surfaces is given.

TL;DR: In this article, the inverse scattering problem for linear canonical differential equations of a special type in the case when the scattering function is a rational matrix-valued function is studied and the main result here is the form of the potential in terms of a realisation of the scattering functions.