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941.
Unconditional uniqueness of solution for $$\dot H^{s_c }$$ critical 4th order NLS in high dimensions 下载免费PDF全文
In this paper, we study the unconditional uniqueness of solution for the Cauchy problem of Ḣsc(0 ≤ sc < 2) critical nonlinear fourth-order Schrödinger equations i∂tu + Δ2u-εu=λ|u|αu. By employing paraproduct estimates and Strichartz estimates, we prove that unconditional uniqueness of solution holds in Ct(I; Ḣsc(Rd)) for d ≥ 11 and min{1-, (8)/(d-4)} ≥ α >(-(d-4)+√4(d-4)2+64)/4. 相似文献
942.
Based on the endpoint Strichartz estimates for the fourth order Schr?dinger equation with potentials for n ≥ 5 by [Feng, H., Soffer, A., Yao, X.: Decay estimates and Strichartz estimates of the fourth-order Schr?dinger operator. J. Funct. Anal., 274, 605–658(2018)], in this paper, the authors further derive Strichartz type estimates with gain of derivatives similar to the one in [Pausader,B.: The cubic fourth-order Schr?dinger equation. J. Funct. Anal., 256, 2473–2517(2009)]. As their applications, we combine the classical Morawetz estimate and the interaction Morawetz estimate to establish scattering theory in the energy space for the defocusing fourth order NLS with potentials and pure power nonlinearity 1 +8/n p 1 +8/(n-4) in dimensions n ≥ 7. 相似文献
943.
On Word Equations Originated from Discrete Dynamical Systems Related to Antisymmetric Cubic Maps with Some Applications 下载免费PDF全文
Elias Abboud 《数学学报(英文版)》2018,34(11):1663-1676
In this article, we solve some word equations originated from discrete dynamical systems related to antisymmetric cubic map. These equations emerge when we work with primitive and greatest words. In particular, we characterize all the cases for which <β1β1>=<β2β2> where β1 and β2 are the greatest words in <<β1>> and <<β2>> of M(n). 相似文献
944.
945.
Oscillatory and asymptotic criteria of third order nonlinear delay dynamic equations with damping term on time scales 下载免费PDF全文
Qinghua Feng 《Journal of Applied Analysis & Computation》2018,8(4):1260-1281
In this paper, we are concerned with oscillatory and asymptotic behavior of third order nonlinear delay dynamic equations with damping term on time scales. By using a generalized Riccati function and inequality technique, we establish some new oscillatory and asymptotic criteria. The established results on one hand extend some known results in the literature, on the other hand unify continuous and discrete analysis as two special cases of an arbitrary time scale. We also present some applications for the established results. 相似文献
946.
Development of a high order discretization scheme for solving fully nonlinear magnetohydrodynamic equations 下载免费PDF全文
A. D. Abin Rejeesh S. Udhayakumar T. V. S. Sekhar Rajagopalan Sivakumar 《Journal of Applied Analysis & Computation》2018,8(1):42-65
We have developed fully fourth order accurate compact finite difference discretization scheme for the Navier-Stokes equations coupled with Maxwell''s equations. The implementation is done in cylindrical polar geometry. Due to the full-MHD modeling of physical flow, the modeled equations are fully nonlinear coupled hydrodynamic equations which are again coupled with Maxwells equations. In our computations, we have accounted for the induced magnetic field in the flow of an electrically conducting fluid in an external magnetic field. The code is tested against available experimental and theoretical data where applicable. It is observed that a smaller grid of $64 \times 64$ is sufficient for weakly nonlinear problems and higher grids up to $512 \times 512$ are needed as the degree of nonlinearities grow in the modeled equation. In the absence of magnetic field, a discontinuity of total drag coefficient and separation length is noted for $Re=73$ which is in agreement with literature. When the magnetic Reynolds number $Rm<1$ separation length decreases linearly with strength of magnetic field on a log-log scale whereas if $Rm>1$, it decreases nonlinearly, at a much faster rate. Thermal boundary layer thickness decreases as the strength of magnetic field increases and it forces the thermal convection to take place in a laminar structure as observed from thermal contour lines. Finally, using divided differences, we establish that the accuracy of the proposed numerical scheme is in fact fourth order. 相似文献
947.
Dynamical behaviour and exact solutions of thirteenth order derivative nonlinear Schr\"{o}dinger equation 下载免费PDF全文
In this paper, we considered the model of the thirteenth order derivatives of nonlinear Schr\"{o}dinger equations. It is shown that a wave packet ansatz inserted into these equations leads to an integrable Hamiltonian dynamical sub-system. By using bifurcation theory of planar dynamical systems, in different parametric regions, we determined the phase portraits. In each of these parametric regions we obtain possible exact explicit parametric representation of the traveling wave solutions corresponding to homoclinic, hetroclinic and periodic orbits. 相似文献
948.
By using sequences generated from fractional-order hyperchaotic systems, a color image encryption scheme is investigated. Firstly, a plain image, which is known to users in advance, is chosen as a secret key to confuse the original image. Then, the confused image is encrypted by the sequences generated from the fractional-order hyperchaotic systems. With this simple encryption method, we can get an encrypted image that is fully scrambled and diused. For chaos-based image cryptosystems, this encryption scheme enhances the security and improves the eectiveness. Furthermore, the cryptosystem resists the dierential attack. Experiments show that the algorithm is suitable for image encryption, and some statistical tests are provided to show the high security in the end 相似文献
949.
M. Bergounioux 《Journal of Functional Analysis》2010,259(9):2296-2332
We provide in this article a refined functional analysis of the Radon operator restricted to axisymmetric functions, and show that it enjoys strong regularity properties in fractional order Hilbert spaces. This study is motivated by a problem of tomographic reconstruction of binary axially symmetric objects, for which we have available one single blurred and noised snapshot. We propose a variational approach to handle this problem, consisting in solving a minimization problem settled in adapted fractional order Hilbert spaces. We show the existence of solutions, and then derive first order necessary conditions for optimality in the form of optimality systems. 相似文献
950.
Sharp bounds on expectations of lifetimes of coherent and mixed systems composed of elements with independent and either identically or non-identically distributed lifetimes are expressed in terms of expected lifetimes of components. Similar evaluations are concluded for the respective mean residual lifetimes. In the IID case, improved inequalities dependent on a concentration parameter connected to the Gini dispersion index are obtained. The results can be used to compare systems with component lifetimes ordered in the convex ordering. In the INID case, some refined bounds are derived in terms of the expected lifetimes of series systems of smaller sizes, and the expected lifetime of single unit for the equivalent systems with IID components. The latter can be further simplified in the case of weak Schur-concavity and Schur-convexity of the system generalized domination polynomial. 相似文献