the relaxation time limit in the compressible euler maxwell equations abstract the aim of this paper is to study multidimensional euler maxwell equations for plasmas with short momentum relaxation time the convergence for the smooth solutions to the compressible euler maxwell equations toward the solutions to the smooth solutions to the drift diffusion equations is proved by means of the maxwell iteration as the relaxation time tends to zero meanwhile the formal derivation of the latter from the former is justified

the asymptotic behavior of globally smooth solutions of the multidimensional isentropic hydrodynamic model for semiconductors abstract in this paper we study the asymptotic behavior of globally smooth solutions of the cauchy problem for the multidimensional isentropic hydrodynamic model for semiconductors in r d we prove that smooth solutions close to equilibrium of the problem converge to a stationary solution exponentially fast as t

relaxation limit and initial layer to hydrodynamic models for semiconductors abstract we study a relaxation limit of a solution to the initial boundary value problem for a hydrodynamic model to a drift diffusion model over a one dimensional bounded domain it is shown that the solution for the hydrodynamic model converges to that for the drift diffusion model globally in time as a physical parameter called a relaxation time tends to zero it is also shown that the solutions to the both models converge to the corresponding stationary solutions as time tends to infinity respectively here the initial data of electron density for the hydrodynamic model can be taken arbitrarily large in the suitable sobolev space provided that the relaxation time is sufficiently small because the drift diffusion model is a coupled system of a uniformly parabolic equation and the poisson equation since the initial data for the hydrodynamic model is not necessarily in momentum equilibrium an initial layer should occur however it is shown that the layer decays exponentially fast as a time variable tends to infinity and or the relaxation time tends to zero these results are proven by the decay estimates of solutions which are derived through energy methods

convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

on mutual information in multipartite quantum states and equality in strong subadditivity of entropy the challenge of equality in the strong subadditivity inequality of entropy is approached via a general additivity of correlation information in terms of nonoverlapping clusters of subsystems in multipartite states density operators a family of tripartite states satisfying equality is derived

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

on the initial boundary value problem for the bipolar hydrodynamic model for semiconductors abstract the global existence and zero relaxation limit results of weak solutions of the initial boundary value problem to the bipolar hydrodynamic model for semiconductors are established by the theory of compensated compactness the boundary conditions of weak solutions in the sense of traces are discussed

the relaxation of the hydrodynamic model for semiconductors to the drift diffusion equations abstract we establish the convergence and consistency of approximate solutions derived by the modified godunov scheme for the initial boundary value problem to a simplified one dimensional hydrodynamic model for semiconductors using the compensated compactness method the traces of weak solutions are introduced and then the weak solutions are proved to satisfy the natural boundary conditions the zero relaxation limit of the hydrodynamic model to the drift diffusion model is proved when the momentum relaxation time tends to zero

projected sequential quadratic programming methods in this paper we introduce and analyze a class of optimization methods called projected sequential quadratic programming sqp methods for the solution of optimization problems with nonlinear equality constraints and simple bound constraints on parts of the variables such problems frequently arise in the numerical solution of optimal control problems projected sqp methods combine the ideas of projected newton methods and sqp methods they use the simple projection onto the set defined by the bound constraints and maintain feasibility with respect to these constraints the iterates are computed using an extension of sqp methods and require only the solution of the linearized equality constraint global convergence of these methods is enforced using a constrained merit function and an armijo like line search we discuss global and local convergence properties of these methods the identification of active indices and we present numerical examples for an optimal control problem governed by a nonlinear h

existence and some limits of stationary solutions to a one dimensional bipolar euler poisson system abstract in this paper we study the stationary flow for a one dimensional isentropic bipolar euler poisson system hydrodynamic model for semiconductor devices this model consists of the continuous equations for the electron and hole densities and their current densities coupled the poisson equation of the electrostatic potential in a bounded interval supplemented by the proper boundary conditions we first show the unique existence of stationary solutions of the one dimensional isentropic hydrodynamic model based on the schauder fixed point principle and the careful energy estimates next we investigate the zero electron mass limit combined zero electron mass and zero hole mass limit the zero relaxation time limit and the debye length quasi neutral limit respectively we also show the strong convergence of the sequence of solutions and give the associated convergence rates

asymptotic behavior of solutions to euler poisson equations for bipolar hydrodynamic model of semiconductors abstract in this paper we study the cauchy problem for 1 d euler poisson system which represents a physically relevant hydrodynamic model but also a challenging case for a bipolar semiconductor device by considering two different pressure functions and a non flat doping profile different from the previous studies gasser et al 2003 7 huang et al 2011 12 huang et al 2012 13 for the case with two identical pressure functions and zero doping profile we realize that the asymptotic profiles of this more physical model are their corresponding stationary waves steady state solutions rather than the diffusion waves furthermore we prove that when the flow is fully subsonic by means of a technical energy method with some new development the smooth solutions of the system are unique exist globally and time algebraically converge to the corresponding stationary solutions the optimal algebraic convergence rates are obtained

subsonic solutions to a one dimensional non isentropic hydrodynamic model for semiconductors the one dimensional stationary full hydrodynamic model for semiconductor devices with non isentropic pressure is studied this model consists of the equations for the electron density electron temperature and electric field in a bounded domain supplemented with boundary conditions the existence of a classical subsonic solution with positive particle density and positive temperature is shown in two situations non constant and constant heat conductivities moreover we prove uniqueness of a classical solution in the latter case the existence proofs are based on elliptic estimates stampacchia truncation methods and fixed point arguments

on the convergence theory of trust region based algorithms for equality constrained optimization in a recent paper dennis el alem and maciel proved global convergence to a stationary point for a general trust region based algorithm for equality constrained optimization this general algorithm is based on appropriate choices of trust region subproblems and seems particularly suitable for large problems this paper shows global convergence to a point satisfying the second order necessary optimality conditions for the same general trust region based algorithm the results given here can be seen as a generalization of the convergence results for trust regions methods for unconstrained optimization obtained by more and sorensen the behavior of the trust radius and the local rate of convergence are analyzed some interesting facts concerning the trust region subproblem for the linearized constraints the quasi normal component of the step and the hard case are presented it is shown how these results can be applied to a class of discretized optimal control problems

convergence of shock capturing schemes for the compressible euler poisson equations we are concerned with approximate methods to construct global solutions with geometrical structure to the compressible euler poisson equations in several space variables a shock capturing numerical scheme is introduced to overcome the new difficulties from the nonlinear resonance of the system and the nonlocal behavior of the source terms the convergence and consistency of the shock capturing scheme for the equations is proved with the aid of the compensated compactness method then new existence results of the global solutions with geometrical structure are obtained the traces of the weak solutions are defined and then the weak solutions are proved to satisfy the boundary conditions the initial data are arbitrarily large withl bounds

smoothing sqp methods for solving degenerate nonsmooth constrained optimization problems with applications to bilevel programs we consider a degenerate nonsmooth and nonconvex optimization problem for which the standard constraint qualification such as the generalized mangasarian fromovitz constraint qualification gmfcq may not hold we use smoothing functions with the gradient consistency property to approximate the nonsmooth functions and introduce a smoothing sequential quadratic programming sqp algorithm under the l infty penalty framework we show that any accumulation point of a selected subsequence of the iteration sequence generated by the smoothing sqp algorithm is a clarke stationary point provided that the sequence of multipliers and the sequence of penalty parameters are bounded furthermore we propose a new condition called the weakly generalized mangasarian fromovitz constraint qualification wgmfcq that is weaker than the gmfcq we show that the extended version of the wgmfcq guarantees the boundedness of the sequence of multipliers and the sequence of penalty parameters and thus guarantees the global c

diffusion relaxation limit of a bipolar hydrodynamic model for semiconductors in the paper we discuss the relaxation limit of a bipolar isentropic hydrodynamical models for semiconductors with small momentum relaxation time with the help of the maxwell iteration we prove that as the relaxation time tends to zero periodic initial value problems of a scaled bipolar isentropic hydrodynamic model have unique smooth solutions existing in the time interval where the classical drift diffusion model has smooth solutions meanwhile we justify a formal derivation of the corresponding drift diffusion model from the bipolar hydrodynamic model

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

zero electron mass limit and zero relaxation time limit in a multi dimensional stationary bipolar euler poisson system in this paper we discuss a two and three dimensional stationary bipolar euler poisson system from plasmas and semiconductor devices we study the zero electron mass limit and the zero relaxation time limit of smooth subsonic solutions for the equations with proper boundary value conditions by using the method of matched asymptotic expansions for each limit we show the existence and uniqueness of profiles and justify the asymptotic expansions up to any order

the role of coherence entropy of physical twin observables in entanglement the concept of physical twin observables pto for bipartite quantum states introduced and proved relevant for quantum information theory in recent work is substantially simplified the relation of observable and state is studied in detail from the point of view of coherence entropy properties of this quantity are further explored it is shown that besides for pure states also for a class of mixed states quantum discord measure of entanglement can be expressed through the coherence entropy of a pto complete in relation to the state

global existence and asymptotic behavior of the solutions to the three dimensional bipolar euler poisson systems abstract in this paper the global existence of smooth solutions for the three dimensional bipolar hydrodynamic model is studied when the initial data are close to a constant state the l 2 decay rate of the solutions is also obtained our approach is based on the detailed analysis of the green function of the linearized system and the elaborate energy estimates as far as we known it is the first result about the existence and l 2 decay rate of global smooth solutions to the multi dimensional bipolar hydrodynamic model

the zero electron mass limit for a stationary nonisentropic hydrodynamic semiconductor model in this paper we study a general multidimensional nonisentropic hydrodynamical model for semiconductors the model is self consistent in the sense that the electric field which forms a forcing term in the momentum equation is determined by the coupled poisson equation for steady state subsonic and potential flows we discuss the zero electron mass limit of system by using the method of asymptotic expansions we show the existence and uniqueness of profiles and justify the asymptotic expansions up to any order

asymptotic expansion in the multi dimensional hydrodynamic model for two carrier plasmas with small parameters this paper is concerned with the two carrier euler poisson equations for plasmas with small parameters we study by means of asymptotic expansions the quasi neutral limit and the zero relaxation time limit for each limit with well prepared initial data we show the existence and uniqueness of an asymptotic expansion up to any order finally we discuss the justification of the limits

global smooth solutions to the multidimensional hydrodynamic model for plasmas with insulating boundary conditions the existence of global smooth solutions to the multidimensional hydrodynamic model for plasmas of electrons and positively charged ions with insulating boundary conditions is shown under the assumption that the initial densities are close to a constant furthermore it is proved that the particle densities converge exponentially fast to the constant steady state

superlinear convergence of affine scaling interior point newton methods for infinite dimensional nonlinear problems with pointwise bounds we develop and analyze a superlinearly convergent affine scaling interior point newton method for infinite dimensional problems with pointwise bounds in lp space the problem formulation is motivated by optimal control problems with lp controls and pointwise control constraints the finite dimensional convergence theory by coleman and li siam j optim 6 1996 pp 418 445 makes essential use of the equivalence of norms and the exact identifiability of the active constraints close to an optimizer with strict complementarity since these features are not available in our infinite dimensional framework algorithmic changes are necessary to ensure fast local convergence the main building block is a newton like iteration for an affine scaling formulation of the kkt condition we demonstrate in an example that a stepsize rule to obtain an interior iterate may require very small stepsizes even arbitrarily close to a nondegenerate solution using a pointwise projection instead we prove superlinear convergence under a weak strict complementarity condition and convergence with mbox q rate 1 under a slightly stronger condition if a smoothing step is available we discuss how the algorithm can be embedded in the class of globally convergent trust region interior point methods recently developed by m heinkenschloss and the authors numerical results for the control of a heating process confirm our theoretical findings

quantum discord a measure of the quantumness of correlations two classically identical expressions for the mutual information generally differ when the systems involved are quantum this difference defines the quantum discord it can be used as a measure of the quantumness of correlations separability of the density matrix describing a pair of systems does not guarantee vanishing of the discord thus showing that absence of entanglement does not imply classicality we relate this to the quantum superposition principle and consider the vanishing of discord as a criterion for the preferred effectively classical states of a system i e the pointer states

existence and uniqueness of stationary solutions to a one dimensional bipolar hydrodynamic model of semiconductors we consider a one dimensional bipolar hydrodynamic model of semiconductors although some results exist for the bipolar case almost their conditions the boundary condition the doping profile etc are far from practical application in the present paper under a condition appropriate for engineering we shall prove the existence and the uniqueness of classical solutions for the stationary problem the most difficult point is to obtain the bounded estimate and the energy estimate

stability of steady state solutions for an isentropic hydrodynamic model of semiconductors of two species abstract we discuss the stability of the steady state solutions for an isentropic hydrodynamic model of semiconductors of two species we consider not only the mass and momentum equations for electrons but also those two equations for holes the recombination effects between electrons and holes are taken into consideration as well we study the case where the doping profile is close to zero and depends on the spacial variable x we shall show that steady state solutions are asymptotically stable

space mapping for optimal control of partial differential equations solving optimal control problems for nonlinear partial differential equations represents a significant numerical challenge due to the tremendous size and possible model difficulties e g nonlinearities of the discretized problems in this paper a novel space mapping technique for solving the aforementioned problem class is introduced analyzed and tested the advantage of the space mapping approach compared to classical multigrid techniques lies in the flexibility of not only using grid coarsening as a model reduction but also employing perhaps less nonlinear surrogates the space mapping is based on a regularization approach which in contrast to other space mapping techniques results in a smooth mapping and thus avoids certain irregular situations at kinks a new broyden update formula for the sensitivities of the space map is also introduced this quasi newton update is motivated by the usual secant condition combined with a secant condition resulting from differentiating the space mapping surrogate the overall algorithm employs a trust region framework for global convergence issues involved in the computations are highlighted and a report on a few illustrative numerical tests is given

stability of steady states of the compressible euler poisson system in r 3 abstract we investigate the global existence and asymptotic behavior of smooth solutions near a non flat steady state to the compressible euler poisson system in r 3 using some concise energy estimates and an interpolation trick we refine the global existence and show that the solution converges to the stationary solution exponentially fast we assume that the h 3 norms of the initial density and velocity are small but the higher derivatives can be arbitrarily large in this sense our method simplifies the proof of hsiao et al 2003 17 and improves the results of it

the decay rate of solution for the bipolar navier stokes poisson system in this paper the cauchy problem for the bipolar navier stokes poisson system is studied we obtain the global existence and the hs decay rate of classical solutions for this problem our approach is mainly based on the analysis of the green s function of the linearized system and some elaborate energy estimates it should be mentioned that with the help of long wave short wave decomposition the decay rate of the higher order derivatives of the solutions is obtained furthermore based on the hs decay rate of the solutions we also give the lp estimate of the solution

asymptotic behavior of the solution to a nonisentropic hydrodynamic model of semiconductors abstract we study the asymptotic behavior of the solution for a hydrodynamic model of semiconductors where the energy equation is included we study the case where the flow is subsonic and the doping profile is close to a negative constant depending on the spacial variablex we shall show that a given steady state solution is asymptotically stable or unstable depending on whether or not the density of the initial data satisfiesp 0 wherepis defined in 3 5

hyperbolic conservation laws with stiff relaxation terms and entropy we study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms reduced systems inviscid and viscous local conservation laws and weakly nonlinear limits are derived through asymptotic expansions an entropy condition is introduced for n n systems that ensures the hyperbolicity of the reduced inviscid system the resulting characteristic speeds are shown to be interlaced with those of the original system moreover the first correction to the reduced system is shown to be dissipative a partial converse is proved for 2 2 systems this structure is then applied to study the convergence to the reduced dynamics for the 2 2 case 1994 john wiley sons inc

weak solutions to isothermal hydrodynamic model for semiconductor devices abstract in this paper the cauchy problem of the isothermal hydrodynamic model for semiconductor devices is investigated the existence of global weak entropy solutions with large initial data is obtained by using a modified fractional step lax friedrichs scheme and the theory of compensated compactness as a byproduct the existence of entropy solutions to the cauchy problem of the isentropic hydrodynamic model for a semiconductor with infinite mass is also proved

large time behavior of the solutions to a hydrodynamic model for semiconductors we establish the global existence of smooth solutions to the cauchy problem for the one dimensional isentropic euler poisson or hydrodynamic model for semiconductors for small initial data in particular we show that as t to infty these solutions converge to the stationary solutions of the drift diffusion equations the existence and uniqueness of stationary solutions to the drift diffusion equations are proved without the smallness assumption

weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift diffusion equation we investigate the relaxation problem for the hydrodynamic isentropic euler poisson system when the momentum relaxation time tends to zero very sharp estimates on the solutions independent of the relaxation time are obtained and used to establish compactness

initial layer and relaxation limit of non isentropic compressible euler equations with damping abstract in this paper we study the relaxation limit of the relaxing cauchy problem for non isentropic compressible euler equations with damping in multi dimensions we prove that the velocity of the relaxing equations converges weakly to the velocity of the relaxed equations while other variables of the relaxing equations converge strongly to the corresponding variables of the relaxed equations we prove that as relaxation time approaches 0 there exists an initial layer for the ill prepared data the convergence of the velocity is strong outside the layer while there is no initial layer for the well prepared data the convergence of the velocity is strong near t 0 the strong convergence rates of all variables are also estimated

relaxation time limit of the multidimensional bipolar hydrodynamic model in besov space abstract in this paper we study a multidimensional bipolar hydrodynamic model for semiconductors or plasmas this system takes the form of the bipolar euler poisson model with electric field and frictional damping added to the momentum equations in the framework of the besov space theory we establish the global existence of smooth solutions for cauchy problems when the initial data are sufficiently close to the constant equilibrium next based on the special structure of the nonlinear system we also show the uniform estimate of solutions with respect to the relaxation time by the high and low frequency decomposition methods finally we discuss the relaxation time limit by compact arguments that is it is shown that the scaled classical solution strongly converges towards that of the corresponding bipolar drift diffusion model as the relaxation time tends to zero

global existence and asymptotic behavior for a multidimensional nonisentropic hydrodynamic semiconductor model with the heat source abstract in this paper a multidimensional nonisentropic hydrodynamic model for semiconductors with the nonconstant lattice temperature is studied the model is self consistent in the sense that the electric field which forms a forcing term in the momentum equation is determined by the coupled poisson equation global existence to the cauchy problem for the multidimensional nonisentropic hydrodynamic semiconductor model with the small perturbed initial data is established and the asymptotic behavior of these smooth solutions is investigated namely that the solutions converge to the general steady state solution exponentially fast as t is obtained moreover the existence and uniqueness of the stationary solutions are investigated

local analysis of a new multipliers method abstract in this paper we introduce a penalty function and a corresponding multipliers method for the solution of a class of nonlinear programming problems where the equality constraints have a particular structure the class models optimal control and engineering design problems with bounds on the state and control variables and has wide applicability the multipliers method updates multipliers corresponding to inequality constraints maintaining their nonnegativity instead of dealing with multipliers associated with equality constraints the basic local convergence properties of the method are proved and a dual framework is introduced we also analyze the properties of the penalized problem related with the penalty function

some limit analysis in a one dimensional stationary quantum hydrodynamic model for semiconductors in this paper we study the steady state hydrodynamic equations for isothermal states including the quantum bohn potential the one dimensional equations for the electron current density and the particle density are coupled self consistently to the poisson equation for the electric potential the quantum correction can be interpreted as a dispersive regularization of the classical hydrodynamic equations in a bounded interval supplemented by the proper boundary conditions we investigate the zero electron mass limit the zero relaxation time limit the debye length quasi neutral limit and some combined limits respectively for each limit we show the strong convergence of the sequence of solutions and give the associated convergence rate

the pointwise estimates of solutions for euler equations with damping in multi dimensions we study the time asymptotic behavior of solutions for the isentropic euler equations with damping in multi dimensions the global existence and pointwise estimates of the solutions are obtained furthermore we obtain the optimal lp 1 p convergence rate of the solution when it is a perturbation of a constant state our approach is based on a detailed analysis of the green function of the linearized system and some energy estimates

convergence of the godunov scheme for a simplified one dimensional hydrodynamic model for semiconductor devices convergence of approximate solutions derived by the godunov scheme for a simplified one dimensional hydrodynamic model for semiconductor devices is established by using the compensated compactness method a global existence theorem is shown and a numerical method for the computation of the physical global solution of this model is provided by this approach

relaxation time limit and initial layer in the isentropic hydrodynamic model for semiconductors abstract this work is concerned with the relaxation time limit in the multidimensional isentropic hydrodynamic model for semiconductors in the critical besov space firstly we construct formal approximations of the initial layer solution to the nonlinear problem by the matched expansion method then assuming some regularity of the solution to the reduced problem and proves the existence of classical solutions in the uniform time interval where the reduced problem has a smooth solution and justify the validity of the formal approximations in any fixed compact subset of the uniform time interval

quantum probability law from environment assisted invariance in terms of pure state twin unitaries zurek s derivation of the born rule from envariance environment assisted invariance is retraced in an attempt to present a more detailed derivation which is extended to encompass the trace rule form of the quantum probability law in its full generality the investigation begins by a review presentation of schmidt decomposition and a detailed and complete theory of twin unitaries which are the other face of envariance and which stand in close connection with twin observables the trace rule tr e with e being an event projector and a quantum state density operator is derived in five stages the first three achieve the same as zurek s derivation of born s rule but in a different way using the full power of twin unitaries stage 4 extends the zurek like derivation to states ray projectors that are not eigenstates of the density operator finally stage 5 utilizes the assumption of continuity of the probability law in the density operators to extend the trace rule to isolated not correlated systems

a quantum measure of coherence and incompatibility the well known two slit interference is understood as a special relation between an observable localization at the slits and a state being on both slits the relation between an observable and a quantum state is investigated in the general case it is assumed that the amount of coherence equals that of the incompatibility between an observable and a state on these grounds an argument is presented that leads to a natural quantum measure of coherence called coherence or incompatibility information its properties are studied in detail making use of the mixing property of relative entropy derived in this paper a precise relation between the measure of coherence of an observable and that of its coarsening is obtained and discussed from the intuitive point of view convexity of the measure is proved and thus the fact that it is an information entity is established a few more detailed properties of the coherence information are derived with a view to investigating the final state entanglement in general repeatable measurement and more importantly general bipartite entanglement in follow ups of this study

the asymptotic behavior of global smooth solutions to the hydrodynamic model for semiconductors with spherical symmetry abstract in this paper we study the asymptotic behavior of the global smooth solutions to the initial boundary value problem for the hydrodynamic model for semiconductors with spherical symmetry we prove that the solution to the problem converges to a stationary solution time asymptotically exponentially fast

a feasible trust region sequential quadratic programming algorithm an algorithm for smooth nonlinear constrained optimization problems is described in which a sequence of feasible iterates is generated by solving a trust region sequential quadratic programming sqp subproblem at each iteration and by perturbing the resulting step to retain feasibility of each iterate by retaining feasibility the algorithm avoids several complications of other trust region sqp approaches the objective function can be used as a merit function and the sqp subproblems are feasible for all choices of the trust region radius global convergence properties are analyzed under various assumptions on the approximate hessian under additional assumptions superlinear convergence to points satisfying second order sufficient conditions is proved

optimal convergence rates to nonlinear diffusion waves for the compressible euler poisson system with damping abstract in this work we study the 1 d isentropic bipolar hydrodynamic model this model takes the form of compressible euler poisson system with nonlinear damping added to the momentum equations under some smallness conditions the solutions to the cauchy problem of the system globally exist and convergence to the nonlinear diffusion waves which are the corresponding solutions of nonlinear parabolic equations given by the darcy s law with a specified initial data the optimal convergence rates are obtained by green function method when the initial perturbation is in l 1 space

on the classical solutions to the hydrodynamic model for semiconductors abstract this paper mainly deals with the multidimensional hydrodynamic model for semiconductors inspired by the previous papers y shizuta s kawashima systems of equations of hyperbolic parabolic type with applications to the discrete boltzmann equation hokkaido math j 14 1985 249 275 s kawashima w a yong dissipative structure and entropy for hyperbolic systems of balance laws arch ration mech anal 174 2004 345 364 w a yong entropy and global existence for hyperbolic balance laws arch ration mech anal 172 2004 247 266 we develop some new frequency localization estimates to establish the global existence and exponential stability of small classical solutions in a class of critical besov spaces which are different from estimates in our recent paper d y fang j xu t zhang global exponential stability of classical solutions to the hydrodynamic model for semiconductors math models methods appl sci 17 2007 1507 1530 furthermore this new method can also be applied to the multidimensional euler equations with damping the analytic tool used is the littlewood paley decomposition

a note on asymptotic behavior of solutions for the one dimensional bipolar euler poisson system abstract in this note we consider a one dimensional bipolar euler poisson system hydrodynamic model this system takes the form of euler poisson with electric field and frictional damping added to the momentum equations when n n paper i gasser l hsiao h l li large time behavior of solutions of the bipolar hydrodynamical model for semiconductors j differential equations 192 2003 326 359 discussed the asymptotic behavior of small smooth solutions to the cauchy problem of the one dimensional bipolar euler poisson system subsequent to i gasser l hsiao h l li large time behavior of solutions of the bipolar hydrodynamical model for semiconductors j differential equations 192 2003 326 359 we investigate the asymptotic behavior of solutions to the cauchy problem with n n n and obtain the optimal convergence rate toward the constant state n 0 n 0 we accomplish the proofs by energy estimates and the decay rates of fundamental solutions of the heat type equations

relaxation time limit in the multi dimensional bipolar nonisentropic euler poisson systems in this paper we consider the multi dimensional bipolar nonisentropic euler poisson systems which model various physical phenomena in semiconductor devices plasmas and channel proteins we mainly study the relaxation time limit of the initial value problem for the bipolar full euler poisson equations with well prepared initial data inspired by the maxwell iteration we construct the different approximation states for the case 1 1 and 1 1 respectively and show that periodic initial value problems of the certain scaled bipolar nonisentropic euler poisson systems in the case 1 1 and 1 1 have unique smooth solutions in the time interval where the classical energy transport equation and the drift diffusive equation have smooth solution moreover it is also obtained that the smooth solutions converge to those of energy transport models at the rate of 2 2 and those of the drift diffusive models at the rate of respectively the proof of these results is based on the continuation principle and the error estimates

large time behavior of euler poisson equations for isothermal fluids with spherical symmetry abstract in this paper the large time behavior of spherically symmetric weak solutions to the multi dimensional isothermal euler poisson system in an annulus is considered when space dimension n 2 it is shown that the weak solutions converge to the unique stationary solution exponentially in time no smallness and regularity conditions are assumed

asymptotic convergence to planar stationary waves for multi dimensional unipolar hydrodynamic model of semiconductors abstract in this study we consider the high dimensional unipolar hydrodynamic model for semiconductors in the form of euler poisson equations based on the results that we have obtained in the first part huang et al 2011 16 for the 1 d case we can further show the stability of planar stationary waves in multi dimensional case utilizing the energy method we obtain the global existence of the solutions of high dimensional euler poisson equations for the unipolar hydrodynamic model and prove that the solutions converge to the planar stationary waves time exponentially

relaxation limit of the one dimensional bipolar euler poisson system in the bound domain in this paper we present a one dimensional bipolar hydrodynamic model from semiconductor devices and plasmas which takes the form of bipolar isothermal euler poisson with electric field and frictional damping added to the momentum equations from proper scaling when the relaxation time in the bipolar euler poisson system tends to zero we can obtain the bipolar drift diffusion equation first we show that the solutions to the initial boundary value problems of the bipolar euler poisson system and the corresponding drift diffusion equation converge to their stationary solutions as time tends to infinity respectively then it is shown that the solution for the bipolar euler poisson equation converges to that of the corresponding bipolar drift diffusion equations as the relaxation time tends to zero with the initial layer

relaxation time limits of non isentropic hydrodynamic models for semiconductors abstract this work deals with non isentropic hydrodynamic models for semiconductors with short momentum and energy relaxation times the high and low frequency decomposition methods are used to construct uniform global classical solutions to cauchy problems of a scaled hydrodynamic model in the framework of critical besov spaces furthermore it is rigorously justified that the classical solutions strongly converge to that of a drift diffusion model as two relaxation times both tend to zero as a by product global existence of weak solutions to the drift diffusion model is also obtained

the bipolar hydrodynamic model for semiconductors and the drift diffusion equations we establish the existence of entropy solutions for a bipolar hydrodynamic model for semiconductors we show also that the limit as the relaxation time goes to zero of an appropriate scaled sequence of entropy solutions is a solution of the classical drift diffusion equations

asymptotic profile in a one dimensional steady state nonisentropic hydrodynamic model for semiconductors we study the stationary flow for a one dimensional nonisentropic hydrodynamic model for semiconductor devices this model consists of the continuous equations for the electron density the electron current density and electron temperature coupled the poisson equation of the electrostatic potential in a bounded interval supplemented by the proper boundary conditions we investigate the zero electron mass limit the zero relaxation time limit and the debye length quasi neutral limit respectively we show the strong convergence of the sequence of solutions and give the associated convergence rate

global solutions to the isothermal euler poisson system with arbitrarily large data abstract we prove the global existence of a solution to the euler poisson system with arbitrarily large data in a one dimensional geometry the pressure law we consider is deduced from an isothermal assumption for the electrons gas in this case nishida has already pointed out that the linear part of the glimm functional is decreasing with respect to time using a glimm scheme he used this property to construct globally defined weak solutions for the euler system with arbitrary large data we follow his outline of proof here a new difficulty arises with the source term due to the electric field a key point is that the glimm scheme is almost conservative this quasi conservation of charge leads to a uniform estimate of the total variation of the electric field this estimate allows to prove the convergence of the scheme