a criterion for the existence of common invariant subspaces of matrices it is shown that square matrices a and b have a common invariant subspace w of dimension k 1 if and only if for some scalar s a c si and b c si are invertible and their kth compounds have a common eigenvector which is a grassmann representative for w t he applicability of this criterion and its ability to yield a basis for the common invariant subspace are investigated 2001 elsevier science inc all rights reserved

convergence of the fractional step lax friedrichs scheme and godunov scheme for the isentropic system of gas dynamics a convergence theorem of the fractional step lax friedrichs scheme and godunov scheme for an inhomogeneous system of isentropic gas dynamics 1 5 3 is established by using the framework of compensated compactness meanwhile a corresponding existence theorem of global solutions with large data containing the vacuum is obtained

l 1 convergence to the barenblatt solution for compressible euler equations with damping we study the asymptotic behavior of compressible isentropic flow through a porous medium when the initial mass is finite the model system is the compressible euler equation with frictional damping as t the density is conjectured to obey the well known porous medium equation and the momentum is expected to be formulated by darcy s law in this paper we prove that any l weak entropy solution to the cauchy problem of damped euler equations with finite initial mass converges strongly in the natural l1 topology with decay rates to the barenblatt profile of the porous medium equation the density function tends to the barenblatt solution of the porous medium equation while the momentum is described by darcy s law the results are achieved through a comprehensive entropy analysis capturing the dissipative character of the problem

dead beat functional observers for discrete time lpv systems with unknown inputs this technical note deals with functional observers for discrete time linear parameter varying lpv systems more specifically dead beat observers for reconstructing linear combinations of the state are proposed the system inputs are assumed to be unknown and the observers reduce to functions of the output over a finite number of time steps the existence of such observers is proven by resorting to the notion of inverse system together with the concepts of maximal robust invariant subspaces and nilpotent semigroups a constructive approach to derive the explicit equations of the observer is provided an example illustrates the efficiency and the computational aspects of the method

common eigenvectors of two matrices abstract a computable criterion is given for two square matrices to possess a common eigenvector as well as a criterion for one matrix to have an eigenvector lying in a given subspace some applications are discussed

l1 convergence rates to the barenblatt solution for the damped compressible euler equations abstract in our previous work 17 it is shown that any l weak entropy solution of damped compressible euler equation converges to the barrenblatt s solution with finite mass in l 1 norm with a convergence rate for 1 3 in this paper by introducing an elaborate iterative method and using the intensive entropy analysis we prove the l 1 convergence to the barrenblatt s solution for any large 3 furthermore we get better l 1 convergence rate for 2 3

convergence of the viscosity method for isentropic gas dynamics a convergence theorem for the method of artificial viscosity applied to the isentropic equations of gas dynamics is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

an algorithmic approach to simultaneous triangularization abstract we present and prove the validity of an algorithm constructing a simultaneous triangularization of a set on n matrices in c n n to do so we first prove that if a set of matrices has a common block decomposition then the set of matrices has a simultaneous triangularization if and only if the blocks on the diagonal have a simultaneous triangularization

existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in eulerian and lagrangian coordinates we prove the existence and compactness stability of entropy solutions for the hyperbolic systems of conservation laws corresponding to the isentropic gas dynamics where the pressure and density are related by a law for any 1 our results considerably extend and simplify the program initiated by diperna and provide a complete existence proof our methods are based on the compensated compactness and the kinetic formulation of systems of conservation laws 1996 john wiley sons inc

nilpotent semigroups for the characterization of flat outputs of switched linear and lpv discrete time systems abstract this paper addresses the problem of flat output characterization for switched linear systems the characterization is also extended to lpv systems the characterization is based on the notion of nilpotent semigroups a complete corresponding recursive algorithm is provided it stops after a finite number of steps bounded by the dimension of the system illustrative examples for the respective class of switched linear and lpv systems highlight the efficiency of the characterization

hyperbolic to parabolic relaxation theory for quasilinear first order systems abstract in this paper we study the limiting behavior of nonhomogeneous hyperbolic systems of balance laws when the relaxed equilibria are described by means of systems of parabolic type in particular we obtain a complete theory for the 2 2 systems of genuinely nonlinear hyperbolic balance laws in 1 d with a strong dissipative term a different method which combines the div curl lemma with accretive operators is then applied to study the limiting profiles in the case of nonhomogeneous isentropic gas dynamics we also investigate relaxation results for some 2 d cases which include the cattaneo model for nonlinear heat conduction and the compressible euler flow moreover convergence result is also obtained for general semilinear systems in 1 d

lp convergence rate to nonlinear diffusion waves for p system with damping abstract in this paper we study the p system with frictional damping and show that the solutions time asymptotically tend to the nonlinear diffusion waves governed by the classical darcy s law by introducing an approximate green function we obtain the optimal l p 2 p convergence rate of the solution which is a perturbation of the nonlinear diffusion wave to the hyperbolic system

convergence to the barenblatt solution for the compressible euler equations with damping and vacuum we study the asymptotic behavior of a compressible isentropic flow through a porous medium when the initial mass is finite the model system is the compressible euler equation with frictional damping as t the density is conjectured to obey the well known porous medium equation and the momentum is expected to be formulated by darcy s law in this paper we give a definite answer to this conjecture without any assumption on smallness or regularity for the initial data we prove that any l weak entropy solution to the cauchy problem of damped euler equations with finite initial mass converges strongly in lp with decay rates to matching barenblatt s profile of the porous medium equation the density function tends to the barenblatt s solution of the porous medium equation while the momentum is described by darcy s law

asymptotic behavior of the solutions to the damped compressible euler equations with vacuum abstract the asymptotic behavior of solutions of the damped compressible euler equations is conjectured to obey to the famous porous media equations pmes the previous works on this topic concern the case away from vacuum where the system is strictly hyperbolic in present paper we prove that the l entropy weak solution with vacuum obtained by the compensated compactness theory converges strongly in l loc p 1 p space to the unique similarity solution of the related pme as time goes to infinity

convergence rate for compressible euler equations with damping and vacuum we study the asymptotic behavior of l weak entropy solutions to the compressible euler equations with damping and vacuum previous works on this topic are mainly concerned with the case away from the vacuum and small initial data in the present paper we prove that the entropy weak solution strongly converges to the similarity solution of the porous media equations in lp r 2 p with decay rates the initial data can contain vacuum and can be arbitrary large a new approach is introduced to control the singularity near vacuum for the desired estimates

compressible euler equations with vacuum abstract in this paper we first show that the regular solutions of compressible euler equations in r 3 with damping will not be global if the initial density function has compact support this implies that c 2 cannot be smooth across the boundary separating the gas and the vacuum after a finite time where c is the speed of sound then we study the local existence of solutions for isentropic gas flow in r when c 0 1 is smooth across using the energy method and the characteristics method

kinetic formulation of the isentropic gas dynamics and p systems we consider the 2 x 2 hyperbolic system of isentropic gas dynamics in both eulerian or lagrangian variables also called the p system we show that they can be reformulated as a kinetic equation using an additional kinetic variable such a formulation was first obtained by the authors in the case of multidimensio nal scalar conservation laws a new phenomenon occurs here namely that the advection velocity is now a combination of the macroscopic and kinetic velocities various applications are given we recover the invariant regions deduce new l estimates using moments lemma and prove l w stability for 7 3

simultaneous reduction of matrices in the presence of a nonderogatory matrix abstract some known results on the question when are two matrices simultaneously similar to matrices in upper triangular form are simplified in the case when one of the matrices is nonderogatory

the common invariant subspace problem an approach via grobner bases let a be an n n matrix it is a relatively simple process to construct a homogeneous ideal generated by quadrics whose associated projective variety parametrizes the one dimensional invariant subspaces of a given a finite collection of n n matrices one can similarly construct a homogeneous ideal again generated by quadrics whose associated projective variety parametrizes the one dimensional subspaces which are invariant subspaces for every member of the collection grobner basis techniques then provide a finite rational algorithm to determine how many points are on this variety in other words a finite rational algorithm is given to determine both the existence and quantity of common one dimensional invariant subspaces to a set of matrices this is then extended for each d to an algorithm to determine both the existence and quantity of common d dimensional invariant subspaces to a set of matrices 2004 published by elsevier inc

direct coupled load verification of modified structural component an analytical vefification method for structural dynamics subject to partial design change is proposed the method can predict time domain structural dynamic responses after the changes are implemented incorporated with the entire structural characteristics including the unchanged portion by using small numbers of modal parameters of the original structure and the modified component the concise computation of the degrees of freedom of the modal representation which are formulated to retain the residual flexibility in the equation of motion can correctly provide changed effects the representation of the component mode synthesis and the force equilibrium between the changed component and the main structure are utilized to develop the algorithm which yields the modal mass stiffness conversion in the component modes applying this method to the spacecraft redesign without the physical property information of the launch vehicle or repetition of coupled load analysis the established algorithm can improve the prediction of the coupled spacecraft and launch vehicle structural dynamics a reanalysis can be implemented using a limited number of available modal parameters from the coupled analysis for the original structure demonstrations applied to simple beam and spacecraft launch vehicle models presented show the effectiveness of the method