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Showing papers in "Journal of Differential Equations in 2002"


Journal ArticleDOI
TL;DR: The purpose of this chapter is to prove existence and uniqueness of the minimizing total variation flow in ℝ N ==================>>\s, when u0 ∈ L loc 1 (L N ) as mentioned in this paper.

281 citations


Journal ArticleDOI
TL;DR: In this article, a free boundary problem for nonlinear magnetohydrodynamics with general large initial data is investigated, and the existence, uniqueness, and regularity of global solutions are established with general initial data in H 1.

218 citations


Journal ArticleDOI
TL;DR: In this paper, the existence and multiplicity results for radial solutions of the Liouville-Bratu-Gelfand problem associated with a class of quasilinear radial operators were determined.

191 citations


Journal ArticleDOI
TL;DR: In this article, the existence and asymptotic stability of a traveling wave with speed c > 0 was studied and it was shown that the traveling wave has the property that U (−∞)=1, U ⊆ R, and lim ξ → ∞ U ( ξ ) e λξ =1.

185 citations


Journal ArticleDOI
TL;DR: In this paper, the authors considered the existence, uniqueness, and asymptotic behavior of mild solutions to stochastic partial functional differential equations with finite delay r>0.

170 citations


Journal ArticleDOI
TL;DR: Alekseenko et al. as mentioned in this paper studied the boundary layer of wall bounded flows in a channel at small viscosity when the boundaries are uniformly noncharacteristic, i.e., there is injection and/or suction everywhere at the boundary.

149 citations


Journal ArticleDOI
TL;DR: In this article, a complete and qualitatively sharp description of heat kernels G of Dirichlet Laplacians on bounded C 1, 1 domains D is given, and the bounds when D is unbounded are also given.

137 citations


Journal ArticleDOI
TL;DR: In this paper, local and global existence for the solutions of the wave equation in bounded domains with nonlinear boundary damping and source terms was studied. And the authors proved local existence of the solutions in the energy space when m > r /( r + 1− p ) or n = 1,2, where p ⩽ m or the initial data are inside the potential well associated to the stationary problem.

134 citations


Journal ArticleDOI
TL;DR: In this paper, the Free Boundary Problem for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity was studied and a local existence result was established when the initial density is of compact support and connects to the vacuum continuously.

134 citations



Journal ArticleDOI
TL;DR: In this article, the trajectories of the damped nonlinear oscillator (HBFC) were studied under the Neumann boundary condition, and it was shown that the trajectory of the system strongly converges, as t→+∞, to the element of minimal norm of the closed convex set S.

Journal ArticleDOI
TL;DR: In this article, the authors considered the equations of motion of compressible viscous fluid in an exterior domain in R 3 and gave the L q − L p estimates for solutions to the linearized equations and showed an optimal decay estimate for solutions for nonlinear problems.

Journal ArticleDOI
TL;DR: In this article, the method of l-trajectories is used to study the large-time behavior of nonlinear evolutionary systems, where solutions suffer from lack of regularity or when the leading elliptic operator is nonlinear.

Journal ArticleDOI
TL;DR: In this article, the authors studied the orbital normal forms for analytic planar vector fields with nilpotent singularity and showed that the Takens normal form is analytic, and they interpreted the coefficients of these moduli in terms of the hidden holonomy group.

Journal ArticleDOI
TL;DR: In this paper, the linear stability of the well-known periodic orbits of Lagrange in the three-body problem was studied and a combination of numerical and analytic methods was used to find the regions of stability in the βe-plane.

Journal ArticleDOI
TL;DR: Daners and Dancer as mentioned in this paper characterized the existence of principal eigenvalues for a general class of linear weighted second order elliptic boundary value problems subject to a very general set of mixed boundary conditions.

Journal ArticleDOI
TL;DR: For a family of functionals in a Banach space, which are possibly non-smooth and depend also on a positive real parameter, the existence of a sequence of critical points is established by mainly adapting a new technique due to Ricceri (2000, J. Appl. Math. as mentioned in this paper ).


Journal ArticleDOI
TL;DR: The existence of the global attractor of a weakly damped, forced Korteweg-de Vries equation in the phase space L 2 (R ) is proved in this article.

Journal ArticleDOI
TL;DR: In this article, the authors rigorously established the existence and stability of the Gierer-Meinhardt system in two dimensions far from homogeneity and showed that Green's function together with its derivatives plays a major role.

Journal ArticleDOI
TL;DR: In this paper, the authors present a priori estimates of the solutions to the second-order elliptic and parabolic interface problems with the explicit appearance of the discontinuous coefficients and the jumps of coefficients across the interface.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the competition model where all the coefficient functions are strictly positive over the underlying spatial region Ω except b (x ), which vanishes in a nontrivial subdomain of Ω, and is positive in the rest of the region.

Journal ArticleDOI
TL;DR: In this paper, sufficient conditions are given for the existence of a solution of a fourth order nonlinear boundary value problem with non-linear boundary conditions, assuming that there exists a strong upper solution-lower solution pair, a concept defined in the paper.

Journal ArticleDOI
TL;DR: In this article, the existence and approximation of the global attractor for second order damped lattice dynamical systems was studied. But the approximation was not considered for the case where the lattice lattice is not convex.

Journal ArticleDOI
Xuefeng Wang1
TL;DR: In this article, a spatial pattern is generated, and it persists on a time scale OðeceÞ but is eventually destroyed: typically uðx; tÞ! 1 uðex; t ðuÞ du 1⁄4 0, for x on 1¼20; 1 as t! 1: It is possible that uð x; t ǫ converges to a or a nonconstant steady state, but this is an unlikely event because all these steady states are unstable.

Journal ArticleDOI
TL;DR: In this article, the existence of homoclinic solutions for a class of fourth-order equations, including the Swift Hohenberg model and the suspension bridge equation, was established.

Journal ArticleDOI
TL;DR: In this article, the form of the differential equations inherited from the symplectic structure and symmetry properties of the Hamiltonian system is analyzed and the effects of time reversing symmetries are included.

Journal ArticleDOI
TL;DR: In this paper, the second part of the study on the competition model where the coefficient functions are strictly positive over the underlying spatial region Ω except b(x), which vanishes in a nontrivial subdomain of Ω, and is positive in the rest of the region.

Journal ArticleDOI
TL;DR: For a bounded domain Ω⊂ R 2, the authors established a concentration-compactness result for the following class of singular Liouville equations: −Δu =e u −4π ∑ j=1 m α j δ p j in Ω where pj∈Ω, αj>0 and δpj denotes the Dirac measure with pole at point pj, j= 1, m.

Journal ArticleDOI
TL;DR: In this article, the authors considered the stability of the rarefaction wave and traveling wave for the Cauchy problem for p-systems with relaxation and showed that the solutions of (E), (I) tend also to the equilibrium rare-faction waves and the traveling waves even if the limits (v±, u±) of the initial data at x =±∞ do not satisfy the equilibrium equation; i.e., u±≠f(v±).