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941.
We consider the Korteweg–de Vries equation with a source. The source depends on the solution as polynomials with constant coefficients. Using the Painlevé test we show that the generalized Korteweg–de Vries equation is not integrable by the inverse scattering transform. However there are some exact solutions of the generalized Korteweg–de Vries equation for two forms of the source. We present these exact solutions. 相似文献
943.
944.
945.
We study the equations of flow of an electrically conductive magnetic fluid, when the fluid is subjected to the action of an external applied magnetic field. The system is formed by the incompressible Navier–Stokes equations, the magnetization relaxation equation of Bloch type and the magnetic induction equation. The system takes into account the Kelvin and Lorentz force densities. We prove the local-in-time existence of the unique strong solution to the system equipped with initial and boundary conditions. We also establish a blow-up criterion for the local strong solution. 相似文献
946.
We study special regularity and decay properties of solutions to the IVP associated to the k-generalized KdV equations. In particular, for datum u 0 ∈ H 3/4+ (?) whose restriction belongs to H l ((b, ∞)) for some l ∈ ?+ and b ∈ ? we prove that the restriction of the corresponding solution u(·, t) belongs to H l ((β, ∞)) for any β ∈ ? and any t ∈ (0, T). Thus, this type of regularity propagates with infinite speed to its left as time evolves. 相似文献
947.
Jessica Lin 《偏微分方程通讯》2015,40(9):1688-1704
This note establishes an interior quantitative lower bound for nonnegative supersolutions of fully nonlinear uniformly parabolic equations. The result may be interpreted as a quantitative version of a growth lemma established by Krylov and Safonov for nonnegative supersolutions of linear uniformly parabolic equations in nondivergence form. Our approach is different, and follows from an application of a reverse Holder inequality. The result is the parabolic analogue of an elliptic regularity estimate established by Caffarelli, Souganidis, and Wang in the stochastic homogenization of fully nonlinear uniformly elliptic equations. 相似文献
948.
949.
Hironobu Sasaki 《偏微分方程通讯》2015,40(11):1959-2004
We study scattering problems for the one-dimensional nonlinear Dirac equation (?t + α?x + iβ)Φ = λ|Φ|p?1Φ. We prove that if p > 3 (resp. p > 3 + 1/6), then the wave operator (resp. the scattering operator) is well-defined on some 0-neighborhood of a weighted Sobolev space. In order to prove these results, we use linear operators D(t)xD(?t) and t?x + x?t ? α/2, where {D(t)}t∈? is the free Dirac evolution group. For the reader's convenience, in an appendix we list and prove fundamental properties of D(t)xD(?t) and t?x + x?t ? α/2. 相似文献
950.
Interpolating minimal energy C1‐Surfaces on Powell–Sabin Triangulations: Application to the resolution of elliptic problems 下载免费PDF全文
M. A. Fortes P. González M. J. Ibáñez M. Pasadas 《Numerical Methods for Partial Differential Equations》2015,31(3):798-821
In this article, we present a method to obtain a C1‐surface, defined on a bounded polygonal domain Ω, which interpolates a specific dataset and minimizes a certain “energy functional.” The minimization space chosen is the one associated to the Powell–Sabin finite element, whose elements are C1‐quadratic splines. We develop a general theoretical framework for that, and we consider two main applications of the theory. For both of them, we give convergence results, and we present some numerical and graphical examples. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 798–821, 2015 相似文献