global existence of classical solutions to the minimal surface equation in two space dimensions with slow decay initial value in this paper we prove the global existence of classical solutions to the cauchy problem for the minimal surface equation in the minkowski space r1 2 with slow decay initial value

dispersion of low energy waves for the generalized benjamin bona mahony equation on considere les equations suivantes u t u x f u x u xxx 0 1 et u t u x f u x u xxt 0 2 avec f r r est c on donne le comportement des solutions ondes a basse energie pour certains f

some observations on the youla form and conjugate normal matrices abstract two square complex matrices a b are said to be unitarily congruent if there is a unitary matrix u such that a ubu t the youla form is a canonical form under unitary congruence we give a simple derivation of this form using coninvariant subspaces for the special class of conjugate normal matrices the associated youla form is discussed

longtime behavior of the kirchhoff type equation with strong damping on rn abstract the paper studies the longtime behavior of the kirchhoff type equation with strong damping on r n u t t m u 2 u u t u u t g x u f x it shows that the related continuous semigroup s t possesses a global attractor which is connected and has finite fractal and hausdorff dimension

monitoring the formation of kernel based topographic maps in a hybrid som kmer model a new lattice disentangling monitoring algorithm for a hybrid self organizing map kernel based maximum entropy learning rule som kmer model is proposed it aims to overcome topological defects owing to a rapid decrease of the neighborhood range over the finite running time in topographic map formation the empirical results demonstrate that the proposed approach is able to accelerate the formation of a topographic map and at the same time to simplify the monitoring procedure

obtaining eringen s length scale coefficient for vibrating nonlocal beams via continualization method abstract eringen s length scale coefficients e 0 are presented herein for initially stressed vibrating nonlocal beams with various boundary conditions the coefficients are obtained by applying the continualization method to the discrete equations of microstructured beam models when compared to another continualized approach that is based on the pade approximant the proposed continualization method which is based on assuming continuous exponential displacement functions for the discrete displacement field is a more straightforward approach for solution unlike the pade approximant approach this latter method needs no sophisticated mathematical manipulations for obtaining the continuous equation moreover the continualization method allows one to directly solve the discrete governing equations for vibration of microstructured beams in the discrete domain rather than solving an approximated continuous equation obtained via the pade approximant by using this method it is found that e 0 1 12 for the buckling case of beams and e 0 1 6 for the vibration case for any combination of end conditions however the coefficients are not the same in the presence of an initial stress for vibrating beams with different boundary conditions

conjugate normal matrices a survey conjugate normal matrices play the same important role in the theory of unitary congruence as the conventional normal matrices do with respect to unitary similarities however unlike the latter the properties of conjugate normal matrices are not widely known motivated by this fact we give a survey of the properties of these matrices in particular a list of more than forty conditions is given each of which is equivalent to a being conjugate normal

nonlocal and nonlinear dispersion in a nonlinear schrodinger type equation exotic solitons and short wavelength instabilities we study the continuum limit of a nonlinear schrodinger lattice model with both on site and inter site nonlinearities describing weakly coupled optical waveguides or bose einstein condensates the resulting continuum nonlinear schrodinger type equation includes both nonlocal and nonlinear dispersion looking for stationary solutions the equation is reduced to an ordinary differential equation with a rescaled spectral parameter and a single parameter interpolating between the nonlocality and the nonlinear dispersion it is seen that these two effects give a similar behaviour for the solutions we find smooth solitons and beyond a critical value of the spectral parameter also nonanalytic solitons in the form of peakons and capons the existence of the exotic solitons is connected to the special properties of the phase space of the equation stability is investigated numerically by calculating eigenvalues and eigenfunctions of the linearized problem and we particularly find that with both nonlocal and nonlinear dispersion simultaneously present all solutions are unstable with respect to a break up into short wavelength oscillations

the initial boundary value problems for a class of nonlinear wave equations with damping term abstract in this paper we study the existence and uniqueness of the global generalized solution and the global classical solution the blowup of the solution and the energy decay of the solutions of the initial boundary value problems for a class of nonlinear wave equations

multiscale coupling in function space weak coupling between molecular dynamics and continuum mechanics we present a function space oriented coupling approach for the multiscale simulation of non linear processes in mechanics using finite elements and molecular dynamics concurrently the key idea is to construct a transfer operator between the different scales on the basis of weighted local averaging instead of using point wise taken values the local weight functions are constructed by assigning a partition of unity to the molecular degrees of freedom shepard s approach this allows for decomposing the micro scale displacements into a low frequency and a high frequency part by means of a weighted l2 projection numerical experiments illustrating the stabilizing effect of our coupling approach are given copyright 2009 john wiley sons ltd

existence and nonexistence of global solutions for a class of nonlinear wave equations of higher order abstract in this paper we investigate the existence and uniqueness of the solution to the cauchy problem for a class of nonlinear wave equations of higher order and prove the existence and nonexistence of global solutions to this problem by a potential well method

asymptotic decomposition of nonlinear dispersive wave equations with dissipation abstract provided 0 solutions of the generalized regularized long wave burgers equation u t u x p u x u xx u xxt 0 that begin with finite energy decay to zero as t becomes unboundedly large consideration is given here to the case where p vanishes at least cubically at the origin in this case solutions of may be decomposed exactly as the sum of a solution of the corresponding linear equation and a higher order correction term an explicit asymptotic form for the l 2 norm of the higher order correction is presented here the effect of the nonlinearity is felt only in the higher order term a similar decomposition is given for the generalized korteweg de vries burgers equation u t u x p u x u xx u xxx 0

a note on an unusual type of polar decomposition motivated by applications in the theory of unitary congruence we introduce the factorization of a square complex matrix a of the form a su where s is complex symmetric and u is unitary we call this factorization a symmetric unitary polar decomposition or an supd it is shown that an supd exists for every matrix a and is always nonunique even the symmetric factor s can be chosen in infinitely many ways nevertheless we show that many properties of the conventional polar decomposition related to normal matrices have their counterparts for the supd provided that normal matrices are replaced with conjugate normal ones

convergence rates of solutions toward boundary layer solutions for generalized benjamin bona mahony burgers equations in the half space this paper is concerned with the initial boundary value problem of the generalized benjamin bona mahony burgers equation in the half space r

global existence and asymptotic behaviour of solutions for the generalized boussinesq equation abstract in this paper we prove the existence and the uniqueness of global solution for the cauchy problem for the generalized boussinesq equation under some assumptions we also show that the l norm of small solution of the cauchy problem for the generalized boussinesq equation decays to zero as t tends to the infinity

a note on the non existence of global solutions of initial boundary value problems for the boussinesq equation utt 3uxxxx uxx 12 u2 xx

on tridiagonal matrices unitarily equivalent to normal matrices abstract in this article the unitary equivalence transformation of normal matrices to tridiagonal form is studied it is well known that any matrix is unitarily equivalent to a tridiagonal matrix in case of a normal matrix the resulting tridiagonal inherits a strong relation between its super and subdiagonal elements the corresponding elements of the super and subdiagonal will have the same absolute value in this article some basic facts about a unitary equivalence transformation of an arbitrary matrix to tridiagonal form are firstly studied both an iterative reduction based on krylov sequences as a direct tridiagonalization procedure via householder transformations are reconsidered this equivalence transformation is then applied to the normal case and equality of the absolute value between the super and subdiagonals is proved self adjointness of the resulting tridiagonal matrix with regard to a specific scalar product is proved properties when applying the reduction on symmetric skew symmetric hermitian skew hermitian and unitary matrices and their relations with e g complex symmetric and pseudo symmetric matrices are presented it is shown that the reduction can then be used to compute the singular value decomposition of normal matrices making use of the takagi factorization finally some extra properties of the reduction as well as an efficient method for computing a unitary complex symmetric decomposition of a normal matrix are given

on the decay of solutions of the generalized benjamin bona mahony equation on etudie le comportement des solutions du probleme aux valeurs initiales u t u x u p u x u xxt 0 x r t o u x 0 x x r p 0 entier on suppose p 4 alors il existe 0 tel que si 1 1 5 0 et x r ou a ne depend pas de x ou t

lq decay rates of solutions for benjamin bona mahony burgers equations abstract this paper studies the asymptotic behavior of solutions for the benjamin bona mahony burgers equations u t u xxt u xx u x u p u x 0 x r t 0 with the initial data u t 0 u 0 x 0 as x under the restrictions u 0 x dx 0 and x u 0 y dy w 2 p 1 1 we obtain more results on the energy decay rates of the solutions in the forms that if p 1 then j x u t l 2 o 1 t 2 j 3 4 for j 0 1 2 p 1 and j x u t l q o 1 t j 2 q 1 2 q for 2 q and j 0 1 2 p 2 furthermore if p 2 then j x u t l q o 1 t j 2 q 1 2 q for 1 q j 0 1 2 p 3 and j x u t t l q o 1 t j 4 q 1 2 q for 2 q j 0 1 2 p 3 which are optimal the proof is dependent on the fourier transform method the energy method and the point wise method of the green function

exponential decay rate of solutions toward traveling waves for the cauchy problem of generalized benjamin bona mahony burgers equations abstract in this paper we investigate the exponential time decay rate of solutions toward traveling waves for the cauchy problem of generalized benjamin bona mahony burgers equations e u t u t x x u x x u x f u x 0 t 0 x r with prescribed initial data i u 0 x u 0 x u as x here 0 r are constants u are two given constants satisfying u u and the nonlinear function f u c 2 r is assumed to be either convex or concave based on the existence of traveling waves the local stability and the algebraic decay rate to traveling waves of solutions to the cauchy problem e and i established in yin et al 2007 13 we show an exponential decay rate of the solutions to the cauchy problem e and i toward the traveling waves mentioned above by employing the space time weighted energy method which was initiated by kawashima and matsumura in 1985 14 and later elaborated by matsumura and nishihara 1994 15 and nishikawa 1998 16

equation free modelling of evolving diseases coarse grained computations with individual based models we demonstrate how direct simulation of stochastic individualbased models can be combined with continuum numericalanalysis techniques to study the dynamics of evolving diseases sidestepping the necessity of obtaining explicit populationlevel models the approach analyses the unavailable in closed form coarse macroscopic equations estimating the necessary quantities through appropriately initialized short bursts of individualbased dynamic simulation we illustrate this approach by analysing a stochastic and discrete model for the evolution of disease agents caused by point mutations within individual hosts building up from classical susceptibleinfectedrecovered and susceptibleinfectedrecoveredsusceptible models our example uses a onedimensional lattice for variant space and assumes a finite number of individuals macroscopic computational tasks enabled through this approach include stationarystate computation coarse projective integration parametric continuation and stability analysis

asymptotic smoothing and attractors for the generalized benjamin bona mahony equation on r 3 abstract we study the asymptotic behavior of the solutions of the benjamin bona mahony equation defined on r 3 we first provide a sufficient condition to verify the asymptotic compactness of an evolution equation defined in an unbounded domain which involves the littlewood paley projection operators we then prove the existence of an attractor for the benjamin bona mahony equation in the phase space h 1 r 3 by showing the solutions are point dissipative and asymptotic compact finally we establish the regularity of the attractor and show that the attractor is bounded in h 2 r 3

a new barrier to the existence of moving kinks in frenkel kontorova lattices an explanation is offered for an observed lower bound on the wave speed of travelling kinks in frenkel kontorova lattices kinks exist at discrete wavespeeds within a parameter regime where there is a resonance with linear waves phonons however they fail to exist even in this codimension one sense whenever there is more than one phonon branch in the dispersion relation inside such bands only quasi kinks with nondecaying oscillatory tails are possible the results are presented for a discrete sine gordon lattice with an onsite potential that has a tunable amount of anharmonicity novel numerical methods are used to trace kinks with topological charge q 1 and 2 in three parameters representing the propagation speed lattice discreteness and anharmonicity although none of the analysis is presented as rigorous mathematics numerical results suggest that the bound on allowable wavespeeds is sharp the results also explain why the vanishing at discrete values of anharmonicity of the peierls nabarro barrier between stationary kinks as discovered by savin et al does not lead to bifurcation of kinks with small wave speed 2003 elsevier b v all rights reserved

decay of solutions of some nonlinear wave equations abstract we study the large time behaviour of solutions to the initial value problem for the korteweg de vries equation and for the regularized long wave equation with a dissipative term appended using energy estimates a maximum principle and a transformation of cole hopf type sharp rates of temporal decay of certain norms of the solution are obtained

large time behavior of solutions to the nonlinear pseudo parabolic equation abstract in this paper we investigate the initial value problem for the nonlinear pseudo parabolic equation global existence and optimal decay estimate of solution are established provided that the initial value is suitably small moreover when n 2 and the nonlinear term f u disappears we prove that the global solutions can be approximated by the linear solution as time tends to infinity when n 1 and the nonlinear term f u disappears we show that as time tends to infinity the global solution approaches the nonlinear diffusion wave described by the self similar solution of the viscous burgers equation

blow up and scattering of solution for a generalized boussinesq equation in this paper we consider the cauchy problem for a class of boussinesq equation we obtain the existence and uniqueness of the local solutions for a class of nonlinearity of the perturbation blow up solutions are obtained furthermore the global existence and nonlinear scattering for small amplitude solutions are established

continuum approach to discreteness we study analytically and numerically continuum models derived on the basis of pade approximations and their effectiveness in modeling spatially discrete systems we not only analyze features of the temporal dynamics that can be captured through these continuum approaches e g shape oscillations radiation effects and trapping but also point out ones that cannot be captured such as peierls nabarro barriers and bloch oscillations we analyze the role of such methods in providing an effective homogenization of spatially discrete as well as of heterogeneous continuum equations finally we develop numerical methods for solving such equations and use them to establish the range of validity of these continuum approximations as well as to compare them with other semicontinuum approximations

cauchy problem of the generalized double dispersion equation abstract in this paper the existence and the uniqueness of the global solution for the cauchy problem of the generalized double dispersion equation are proved the blow up of the solution for the cauchy problem of the generalized double dispersion equation is discussed by the concavity method under some conditions

asymptotic behavior of classical solutions to the compressible navier stokes poisson equations in three and higher dimensions abstract in this paper we consider the initial value problem for the compressible navier stokes poisson equations in three and higher dimensions firstly global existence and new decay estimate of classical solutions are established the proof is mainly based on the decay properties of solution operator to the compressible navier stokes poisson equations which may be derived from the pointwise estimate of the solution operator to a linear wave equation that is corresponding to the density function while the pointwise estimate of solution operator to the linear wave equation may be established by an energy method in the fourier space the method is different from those in previous works on decay estimate of solutions to compressible navier stokes poisson equations finally asymptotic profile of the solution to the corresponding linear problem is also investigated

normal matrices an update abstract a list of seventy conditions on an n n complex matrix a equivalent to its being normal published nearly ten years ago by grone johnson sa and wolkowicz has proved to be very useful hoping that in an extended form it will be even more helpful we compile here another list of about twenty conditions they either have been overlooked by the authors of the original list or have appeared during the last decade

convergence of the unitary qr algorithm with a unimodular wilkinson shift in applying the qr algorithm to compute the eigenvalues of a unitary hessenberg matrix a projected wilkinson shift of unit modulus is proposed and proved to give global convergence with at least a quadratic asymptotic rate for the qr iteration experimental testing demonstrates that the unimodular shift produces more efficient numerical convergence

convergence to diffusion waves of solutions for viscous conservation laws we study the large time behavior of solutions of viscous conservation laws it is shown that solutions tend to diffusion waves which are constructed based on the heat equation and burgers equation the convergence is in thelp 1 p sense and is obtained as a consequence of thel2 decay of the difference between the solution and its asymptotic state of diffusion waves

kawahara dynamics in dispersive media abstract in a previous paper it was shown that in the long wave limit the water wave problem without surface tension can be described approximately by two decoupled kdv equations here we study a model problem and prove that in a degenerate case which occurs for the water wave problem with surface tension and near other codimension two points at which the coefficient in front of the leading order dispersive term in the equation of motion vanishes the long wave limit can be rigorously approximated by two decoupled kawahara equations

potential method applied to boussinesq equation in this paper a solution of the nonlinear boussinesq equation is presented using the potential similarity transformation method the equation is first written in a conserved form a potential function is then assumed reducing it to a system of equations which is further solved through the group transformation method new transformations are found

decay estimate of solutions to the sixth order damped boussinesq equation abstract in this paper we consider the initial value problem for the sixth order damped boussinesq equation we prove the global existence and asymptotic behavior of solutions for all space dimensions n 1 provided that the initial value is suitably small moreover we show that the solution can be approximated by the linear solution as time tends to infinity for n 2 the result slightly improves the result obtained by wang 2012 3

performance and accuracy of lapack s symmetric tridiagonal eigensolvers we compare four algorithms from the latest lapack 3 1 release for computing eigenpairs of a symmetric tridiagonal matrix these include qr iteration bisection and inverse iteration bi the divide and conquer method dc and the method of multiple relatively robust representations mr our evaluation considers speed and accuracy when computing all eigenpairs and additionally subset computations using a variety of carefully selected test problems our study includes a variety of today s computer architectures our conclusions can be summarized as follows 1 dc and mr are generally much faster than qr and bi on large matrices 2 mr almost always does the fewest floating point operations but at a lower mflop rate than all the other algorithms 3 the exact performance of mr and dc strongly depends on the matrix at hand 4 dc and qr are the most accurate algorithms with observed accuracy o sqrt n varepsilon the accuracy of bi and mr is generally o n varepsilon 5 mr is preferable to bi for subset computations

blow up of solutions of pseudoparabolic equations we obtain sufficient conditions for the blow up of solutions of the initial boundary value problem for nonlinear pseudoparabolic equation involving nonlinear convective term

global existence and asymptotic behavior of classical solutions of quasilinear hyperbolic systems with linearly degenerate characteristic fields abstract in this paper we study the global existence and the asymptotic behavior of classical solution of the cauchy problem for quasilinear hyperbolic system with constant multiple and linearly degenerate characteristic fields we prove that the global c 1 solution exists uniquely if the bv norm of the initial data is sufficiently small based on the existence result on the global classical solution we show that when the time t tends to the infinity the solution approaches a combination of c 1 traveling wave solutions finally we give an application to the equation for time like extremal surfaces in the minkowski space time r 1 n

singular value decompositions of complex symmetric matrices abstract if the complex square matrix a is symmetric i e a at then it has a symmetric singular value decomposition a q qt an algorithm is presented for the computation of this decomposition

two conjugate gradient type methods for unsymmetric linear equations we propose two new conjugate gradient type methods for the solution of sparse unsymmetric linear systems we present a new tridiagonalization process for unsymmetric matrices that is closely related to the lanczos process we use orthogonal factorizations of the tridiagonal matrix to derive the new algorithms usymlq and usymqr in the same fashion as symmlq and minres c c paige and m a saunders solution of sparse indefinite systems of linear equations siam j numer anal 12 1975 pp 617 629 for symmetric matrices some numerical results for the new methods and comparisons with other methods are presented

gmres type methods for inconsistent systems abstract the behavior of iterative methods of gmres type when applied to singular possibly inconsistent linear systems is discussed and conditions under which these methods converge to the least squares solution of minimal norm are presented error bounds for the computed iterates are shown this paper complements previous work by brown and walker p n brown h f walker siam j matrix anal appl 18 1997 37 51

a regularized model equation for discrete breathers in anharmonic lattices with symmetric nearest neighbor potentials abstract we propose a regularized continuum model equation for describing discrete breathers or intrinsic localized modes in one dimensional anharmonic lattices with symmetric nearest neighbor potentials exact stationary breather solutions with purely hard quartic anharmonicity as well as approximate stationary breather solutions in the general case are found the application of the multiple scales analysis indicates the movability of the small amplitude breather solutions the results of numerical simulations for the model equation fully support the analytical solutions as regards the breather breather collisions the continuum model shares many common features with its discrete counterpart which provides an opportunity to clarify the energy exchange mechanism for collisions between discrete breathers in lattices

the decay rates of solutions of generalized benjamin bona mahony equations in multi dimensions abstract in this paper we study the decay rates of the generalized benjamin bona mahony equations in multi dimensional space by using fourier analysis for low frequencies and by applying the energy method for high frequencies we obtain the l 2 convergence rates of the solution when the initial data is in a bounded subset of the phase space h 1 r n n 3 the optimum decay rate is obtained in our results since it is the same as for the heat equation

solitonic solutions for a variable coefficient variant boussinesq system in the long gravity waves variable coefficient variant boussinesq vcvb system is able to describe the nonlinear and dispersive long gravity waves traveling in two horizontal directions with varying depth in this paper with symbolic computation a lax pair associated with the vcvb system under some constraints for variable coefficients is derived and based on the lax pair two sorts of basic darboux transformations are presented by applying the darboux transformations some solitonic solutions are obtained with the relevant constraints given in the text in addition the vcvb system is transformed to a variable coefficient broer kaup system solitonic solutions and procedure of getting them could be helpful to solve the nonlinear and dispersive problems in fluid dynamics

asymptotic behavior and blow up of solutions to a nonlinear evolution equation of fourth order abstract in this paper the asymptotic behavior of the solution to the initial boundary value problem for a nonlinear evolution equation of fourth order 1 u t t a 1 u x x a 2 u x x t a 3 u x x t t u x x is studied the sufficient conditions for blow up of the solutions to the initial boundary value problems for eq 1 are given

global existence and asymptotic behavior of solutions to a nonlinear wave equation of fourth order in this paper we focus on the cauchy problem for a nonlinear wave equation of fourth order in n dimensional space n 1 the decay structure of which is of regularity loss property based on the decay estimate of solutions to the linear problem we introduce a set of time weighted sobolev spaces by using the contraction mapping theorem we obtain the global in time existence and the optimal decay estimates of solutions to the cauchy problem under smallness assumption on the initial data

eigenvalue computation for unitary rank structured matrices in this paper we describe how to compute the eigenvalues of a unitary rank structured matrix in two steps first we perform a reduction of the given matrix into hessenberg form next we compute the eigenvalues of this resulting hessenberg matrix via an implicit qr algorithm along the way we explain how the knowledge of a certain shift correction term to the structure can be used to speed up the qr algorithm for unitary hessenberg matrices and how this observation was implicitly used in a paper due to william b gragg we also treat an analogue of this observation in the hermitian tridiagonal case

small amplitude solutions of the generalized imbq equation in this paper the global existence of small amplitude solution for the cauchy problem of the multidimensional generalized imbq equation is proved moreover we obtain a nonlinear scattering result of the cauchy problem of the imbq equation for small initial data

global existence and asymptotic behavior of solutions for a semi linear wave equation abstract in this paper we investigate the initial value problem for a semi linear wave equation in n dimensional space based on the decay estimate of solutions to the corresponding linear equation we define a set of time weighted sobolev spaces under small condition on the initial value we prove the global existence and asymptotic behavior of the solution in the corresponding sobolev spaces by the contraction mapping principle

decay estimates for the solutions of some nonlinear evolution equations abstract we study decay estimates for the solutions and their derivatives to the initial value problems for some generalized nonlinear evolution equations which have lower order diffusion terms

global existence and optimal time decay estimates of solutions to the generalized double dispersion equation on the framework of besov spaces abstract we investigate the initial value problem for the generalized double dispersion equation in any dimensions inspired by 28 for the hyperbolic system of first order pdes we develop littlewood paley pointwise energy estimates for the dissipative wave equation of high order furthermore with aid of the frequency localization duhamel principle we establish the global existence and optimal decay estimates of solutions in spatially critical besov spaces our results could hold true for any dimensions n 1 indeed the proofs are different in case of high dimensions and low dimensions owing to interpolation tricks

global existence of solution of cauchy problem for nonlinear pseudo parabolic equation abstract in this paper we prove that the cauchy problem for the nonlinear pseudo parabolic equation v t v x x t v x x v x f v x v x x g v g v x x admits a unique global generalized solution in c 1 0 h s r a unique global classical solution and asymptotic behavior of the solution we also prove that the cauchy problem for the equation v t v x x t v x x g v g v x x has a unique global generalized solution in c 1 0 w m p r l r a unique global classical solution and asymptotic behavior of the solution

batch map extensions of the kernel based maximum entropy learning rule in this letter two batch map extensions are described for the kernel based maximum entropy learning rule kmer in the first the weights are iteratively set to weighted component wise medians while in the second the generalized median is used enabling kmer to process symbolic data simulations are performed to illustrate the extensions

the pointwise estimates of solutions for semilinear dissipative wave equation in multi dimensions abstract in this paper we study the global in time existence and the pointwise estimates of solutions to the cauchy problem for the dissipative wave equation in multi dimensions using the fixed point theorem we obtain the global existence of the solution in addition the pointwise estimates of the solution are obtained by the method of the green function furthermore we obtain the l p 1 p convergence rate of the solution

existence and asymptotic stability of time periodic solutions to the generalized double dispersion equation with periodic external force abstract in this paper we investigate the generalized double dispersion equation with periodic external force in r n we prove the existence and uniqueness of time periodic solutions that have the same period as the external force in some suitable function space for the space dimension n 3 the proof is based on the spectral analysis for the solution operator and the contraction mapping theorem in addition we also discuss the time asymptotic stability of the time periodic solutions by continuous argument

temporal asymptotic behavior of solutions of the benjamin ono burgers equation abstract we study certain similarity solutions of the benjamin ono burgers bob equation and their role in the asymptotic behavior of the general solution for small initial data in l 1 r we prove that a solution of the bob equation exists in bc r l 1 r and depends continuously on its initial data results about existence uniqueness regularity and spatial asymptotics of solutions of a similarity reduction of the bob equation are proved furthermore the solutions of the bob equation are proved to converge as t to appropriate similarity solutions faster than the typically sharp rate of decay of the solutions

product eigenvalue problems many eigenvalue problems are most naturally viewed as product eigenvalue problems the eigenvalues of a matrix a are wanted but a is not given explicitly instead it is presented as a product of several factors a a k a k 1 cdots a 1 usually more accurate results are obtained by working with the factors rather than forming a explicitly for example if we want eigenvalues vectors of b t b it is better to work directly with b and not compute the product the intent of this paper is to demonstrate that the product eigenvalue problem is a powerful unifying concept diverse examples of eigenvalue problems are discussed and formulated as product eigenvalue problems for all but a couple of these examples it is shown that the standard algorithms for solving them are instances of a generic gr algorithm applied to a related cyclic matrix

a unitary hessenberg qr based algorithm via semiseparable matrices in this paper we present a novel method for solving the unitary hessenberg eigenvalue problem in the first phase an algorithm is designed to transform the unitary matrix into a diagonal plus semiseparable form then we rely on our earlier adaptation of the qr algorithm to solve the dpss eigenvalue problem in a fast and robust way exploiting the structure of the problem enables us to yield a quadratic time using a linear memory space nonetheless the algorithm remains robust and converges as fast as the customary qr algorithm numerical experiments confirm the effectiveness and the robustness of our approach

long time behavior of solutions to the compressible mhd system in multi dimensions abstract in this paper we consider the initial value problem for the compressible mhd system in multi dimensions under suitable conditions on the initial value the global existence and long time behavior of classical solutions are established moreover we also show that the solution can be approximated by the linear solution as time tends to infinity the proof is based on the decay properties of solution operator to the compressible mhd system which may be given in terms of the heat kernel and the solution operator to a linear wave equation that is corresponding to the density function the decay properties of solution operators to the compressible mhd system may be derived from the pointwise estimate of solution operator to the linear wave equation finally asymptotic profile to the linear system is also established

initial boundary value problem for a class of semilinear pseudo parabolic equations with logarithmic nonlinearity abstract in this paper we study the initial boundary value problem for a class of semilinear pseudo parabolic equations with logarithmic nonlinearity by using the logarithmic sobolev inequality and a family of potential wells we obtain the existence of global solution blow up at and behavior of vacuum isolation of solutions on the other hand the asymptotic behavior of solutions is also discussed our result implies that the polynomial nonlinearity is important for the solutions of such kinds of semilinear pseudo parabolic equations to be blow up in finite time

decay and scattering of small solutions of a generalized boussinesq equation abstract we study the long time behavior of small solutions of the initial value problem for a generalized boussinesq equation we obtain a lower bound for the degrees of nonlinearity which allows us to establish a nonlinear scattering result for small perturbations that is the small solutions of the nonlinear problem behave asymptotically like the solution of the associated linear problem under certain hypotheses we can construct a scattering operator for the boussinesq equation which carries a neighborhood of 0 in the energy space x into x

on a condensed form for normal matrices under finite sequences of elementary unitary similarities abstract it is generally known that any hermitian matrix can be reduced to a tridiagonal form by a finite sequence of unitary similarities namely householder reflections recently a bunse gerstner and l elsner have found a condensed form to which any unitary matrix can be reduced again by a finite sequence of householder transformations this condensed form can be considered as a pentadiagonal or block tridiagonal matrix with some additional zeros inside the band we describe such a condensed form or more precisely a set of such forms for general normal matrices where the number of nonzero elements does not exceed o n 3 2 n being the order of the normal matrix given two approaches to constructing the condensed form are outlined the first approach is a geometrical lanczos type one where we use the so called generalized krylov sequences the second more constructive approach is an elimination process using householder reflections our condensed form can be thought of as a variable bandwidth form an interesting feature of it is that for normal matrices whose spectra lie on algebraic curves of low degree the bandwidth is much smaller

derivation of a class of training algorithms a novel derivation is presented of t kohonen s topographic mapping training algorithm self organization and associative memory 1984 based upon an extension of the linde buzo gray lbg algorithm for vector quantizer design thus a vector quantizer is designed by minimizing an l sub 2 reconstruction distortion measure including an additional contribution from the effect of code noise which corrupts the output of the vector quantizer the neighborhood updating scheme of kohonen s topographic mapping training algorithm emerges as a special case of this code noise model this formulation of kohonen s algorithm is a specific instance of the robust hidden layer principle which stabilizes the internal representations chosen by a network against anticipated noise or distortion processes

nonlinear stability of generalized benjamin bona mahony burgers shock profiles in several dimensions abstract this paper is concerned with nonlinear stability of planar viscous shock profiles of the generalized benjamin bona mahony burgers equations in two dimensions our analysis is motivated by j goodman s work 1989 4 on the nonlinear stability of scalar viscous shock profiles in two dimensions and is based on some new decay estimates on the planar viscous shock profiles of the generalized benjamin bona mahony burgers equations

decay properties of solutions to the cauchy problem for the damped wave equation with absorption abstract we consider the cauchy problem for the damped wave equation with absorption u t t u u t u p 1 u 0 t x r r n the behavior of u as t is expected to be the same as that for the corresponding heat equation t p 1 0 t x r r n which has the similarity solution w a t x with the form t 1 p 1 f x t depending on a lim x x 2 p 1 f x 0 provided that p is less than the fujita exponent p c n 1 2 n in this paper as a first step if 1 p p c n and the data u 0 u 1 x decays exponentially as x without smallness condition the solution is shown to decay with rates as t u t l 2 u t l p 1 u t l 2 o t 1 p 1 n 4 t 1 p 1 n 2 p 1 t 1 p 1 1 2 n 4 those of which seem to be reasonable because the similarity solution w a t x has the same decay rates as for the proof the weighted l 2 energy method will be employed with suitable weight similar to that in todorova and yordanov y todorova b yordanov critical exponent for a nonlinear wave equation with damping j differential equations 174 2001 464 489

lower bounds of rates of decay for solutions to the navier stokes equations where a p 3 2 p 1 and the constant c depends on the l2 and lnorms of the initial data u0 this paper deals with the more subtle problem of deriving lower bounds on the energy decay rates we show that for a certain class of initial data the solutions u x t to the 2d and 3d navier stokes equations admit an algebraic lower bound on the energy decay specifically there are two cases to consider in the first case the average of the initial data f u0 dx is nonzero this case was treated in the earlier paper 5 where it was established that

asymptotic profile of solutions to the double dispersion equation abstract in this paper we investigate the initial value problem for the double dispersion equation in r n decay estimate and asymptotic profile of solutions to the corresponding linear problem are established the asymptotic profile of solutions to the corresponding linear problem is given by the convolution of the fundamental solutions of heat and free wave equations moreover the asymptotic profile of solutions shows the decay estimate of solutions to the corresponding linear problem obtained in this paper is optimal under some conditions finally global existence and optimal decay estimate of solutions to the nonlinear problem are also established

global existence of classical solutions to the minimal surface equation with slow decay initial value in this paper we prove that the global existence of classical solutions to the cauchy problem for the minimal surface equation with slow decay initial value in minkowskian space time