Archive for Rational Mechanics and Analysis
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Superfluid mechanics for a high density of vortex lines
Archive for Rational Mechanics and Analysis - Tập 66 - Trang 43-71 - 1977
There are two well known theories to describe the motion and thermodynamics of superfluids when a large number of quantized vortex lines are present and when the phenomena under study are on scales large compared with the vortex line spacing. These works have been criticised on the grounds that their governing equations for the smoothly varying, spatially averaged, fields do not satisfy the accept...... hiện toàn bộ
Special Fast Diffusion with Slow Asymptotics: Entropy Method and Flow on a Riemannian Manifold
Archive for Rational Mechanics and Analysis - Tập 196 - Trang 631-680 - 2009
We consider the asymptotic behaviour of positive solutions u(t, x) of the fast diffusion equation
$${u_t=\Delta (u^{m}/m)= {\rm div}\,(u^{m-1} \nabla u)}$$
posed for
$${x\in\mathbb R^d}$$
, t > 0, with a precise...... hiện toàn bộ
Monotonicity and 1-Dimensional Symmetry for Solutions of an Elliptic System Arising in Bose–Einstein Condensation
Archive for Rational Mechanics and Analysis - Tập 213 - Trang 287-326 - 2014
We study monotonicity and 1-dimensional symmetry for positive solutions with algebraic growth of the following elliptic system:
$$\left\{\begin{array}{ll} -\Delta u = -u \upsilon^2 &\quad {\rm in}\, \mathbb{R}^N\\
-\Delta \upsilon= -u^2 \upsilon &\quad {{\rm in}\, \mathbb{R}^N},\end{array}\right.$$
...... hiện toàn bộ
On the Symmetry of Minimizers
Archive for Rational Mechanics and Analysis - Tập 192 - Trang 311-330 - 2008
For a large class of variational problems we prove that minimizers are symmetric whenever they are C
1.
Asymptotic series solutions of some nonlinear parabolic equations with a small parameter
Archive for Rational Mechanics and Analysis - Tập 35 - Trang 284-298 - 1969
Asymptotic representations for differential equations with a regular singular point
Archive for Rational Mechanics and Analysis - Tập 3 - Trang 206-218 - 1959
Multiple Brake Orbits and Homoclinics in Riemannian Manifolds
Archive for Rational Mechanics and Analysis - Tập 200 - Trang 691-724 - 2010
Let (M, g) be a complete Riemannian manifold,
$${\Omega\subset M}$$
an open subset whose closure is homeomorphic to an annulus. We prove that if ∂Ω is smooth and it satisfies a strong concavity assumption, then there are at least two distinct geodesics in
...... hiện toàn bộ
Paralinearization of the Muskat Equation and Application to the Cauchy Problem
Archive for Rational Mechanics and Analysis - Tập 237 - Trang 545-583 - 2020
We paralinearize the Muskat equation to extract an explicit parabolic evolution equation having a compact form. This result is applied to give a simple proof of the local well-posedness of the Cauchy problem for rough initial data, in homogeneous Sobolev spaces $$\dot{H}^1(\mathbb {R})\cap \dot{H}^s(\mathbb {R})$$ with $$s>3/2$$. This paper is essentially self-contained and does not rely on genera...... hiện toàn bộ
Bemerkung zum maximumprinzip für den gradienten einer elliptischen differentialgleichung mit nichtkonstanten Koeffizienten
Archive for Rational Mechanics and Analysis - Tập 63 - Trang 87-88 - 1976
Tổng số: 3,465
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