dissipative boundary conditions for 2 2 hyperbolic systems of conservation laws for entropy solutions in bv in this article we investigate the bv stability of 2 2 hyperbolic systems of conservation laws with strictly positive velocities under dissipative boundary conditions more precisely we derive sufficient conditions guaranteeing the exponential stability of the system under consideration for entropy solutions in bv our proof is based on a front tracking algorithm used to construct approximate piecewise constants solutions whose bv norms are controlled through a lyapunov functional this lyapunov functional is inspired by the one proposed in j glimm s seminal work j glimm comm pure appl math 18 697 715 1965 modified with some suitable weights in the spirit of the previous works j m coron g bastin and b d andrea novel siam j control optim 47 3 1460 1498 2008 and j m coron b d andrea novel and g bastin ieee trans automat control 52 1 2 11 2007

on the controllability of the non isentropic 1 d euler equation in this paper we examine the question of the boundary controllability of the one dimensional non isentropic euler equation for compressible polytropic gas in the context of weak entropy solutions we consider the system in eulerian coordinates and the one in lagrangian coordinates we obtain for both systems a result of controllability toward constant states with the limitation gamma frac 5 3 on the adiabatic constant for the lagrangian system the solutions that we obtain remain of small total variation in space if the initial condition is itself of sufficiently small total variation

on the boundary controllability of first order hyperbolic systems abstract we discuss some results concerning the boundary controllability and stabilizability of a hyperbolic system of conservation laws u t f u x 0 t 0 x 0 1 where we regard the boundary data or a partial number of their components as boundary input controls in particular we consider the problem of the global exact boundary controllability of a first order linear hyperbolic system with constant coefficients relative to the linear boundary conditions under generic orthogonality assumptions on the boundary and control matrices and assuming a non resonance condition of the characteristic speeds we show that one can steer in finite time the solution from any initial condition l 1 to any terminal state l 1 even in the case where only a partial control of the boundary values is available

analysis and control of a scalar conservation law modeling a highly re entrant manufacturing system abstract in this paper we study a scalar conservation law that models a highly re entrant manufacturing system as encountered in semi conductor production as a generalization of coron et al 2010 14 the velocity function possesses both the local and nonlocal character we prove the existence and uniqueness of the weak solution to the cauchy problem with initial and boundary data in l we also obtain the stability continuous dependence of both the solution and the out flux with respect to the initial and boundary data finally we prove the existence of an optimal control that minimizes in the l p sense with 1 p the difference between the actual out flux and a forecast demand over a fixed time period

exact controllability for the semilinear mindlin timoshenko system abstract we consider the dynamical one dimensional mindlin timoshenko system for beams we obtain a global exact controllability result for this semilinear system with superlinear nonlinearities for this purpose we establish an observability estimate for the linearized system with bounded potentials moreover we obtain an explicit estimate of the observability constant in terms of the norms of the potentials such an estimate is obtained by a combination of a pointwise estimate a global carleman estimate for hyperbolic differential operators and an analysis of the regularity of solutions of a auxiliary optimal control problem the controllability of the semilinear system is proved using the hilbert uniqueness method hum and a fixed point technique

brief paper complete controllability of impulsive stochastic integro differential systems this paper is concerned with the controllability of impulsive stochastic integro differential systems sufficient conditions of complete controllability for impulsive stochastic integro differential systems are obtained by using schaefer s fixed point theorem a numerical example is provided to show the effectiveness of the proposed results

controllability and stabilization of a conservation law modeling a highly re entrant manufacturing system abstract in this paper we study the controllability and stabilization for a scalar conservation law modeling a highly re entrant manufacturing system with local and nonlocal velocity we prove a local state controllability result i e there exists a control that drives the solution from any given initial condition to any desired final condition in a certain time period provided that the initial and final data are both close to the origin a local result on nodal profile controllability is also given i e for any initial data and any given out flux in a neighborhood of the origin there exists a control under which the solution starts from any initial data reaches exactly any desired out flux over a fixed time period besides using a lyapunov function approach we can stabilize the system to the origin exponentially by output feedback control

exact boundary controllability for quasilinear wave equations a unified constructive method is given to establish the local exact boundary controllability for one dimensional quasilinear wave equations with boundary conditions of different types

stabilization and controllability of first order integro differential hyperbolic equations in the present article we study the stabilization of first order linear integro differential hyperbolic equations for such equations we prove that the stabilization in finite time is equivalent to the exact controllability property the proof relies on a fredholm transformation that maps the original system into a finite time stable target system the controllability assumption is used to prove the invertibility of such a transformation finally using the method of moments we show in a particular case that the controllability is reduced to the criterion of fattorini

on the optimization of the initial boundary value problem for a conservation law abstract in the present note the theory of shift differentiability for the cauchy problem is extended to the case of an initial boundary value problem for a conservation law this result allows to exhibit an euler lagrange equation to be satisfied by the extrema of integral functionals defined on the solutions of initial boundary value problems of this kind

a note on valued division algebras let d be a finite dimensional division algebra with center f and let b be a valuation ring of d i e xeb or x 1 e b holds for all nonzero x in d then b is called an extension of v f b let s be the set of all extensions of v to d and let p b be the group of all bijections of s which are induced by the inner automorphisms of d in this note we investigate p b it is shown that p b is solvable and an upper bound for p b is given finally theorem 4 5 gives a necessary and sufficient condition for b such that p b is equal to this bound

exact boundary controllability for 1 d quasilinear wave equations in this paper we present a unified constructive method to establish the local exact boundary controllability for 1 d quasilinear wave equations with boundary conditions of various types

global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws ii in this paper by a new constructive method the authors reprove the global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws with linearly degenerate characteristics it is shown that the system with nonlinear boundary conditions is globally exactly boundary controllable in the class of piecewise c1 functions in particular the authors give the optimal control time of the system finally a new example belonging to this kind of system is also provided

global controllability of nonviscous and viscous burgers type equations in this paper we deal with both nonviscous and viscous burgers type equations on a bounded interval we study the global exact controllability of these equations when we have three controls one control is the right member of the equation and is constant with respect to the space variable the two others are the boundary values for a first time we are interested in nonviscous burgers type equations and we prove their global exact controllability for every time t 0 with such controls thanks to the return method then we prove the global exact controllability of the viscous burgers equation for every time t 0

exact internal controllability of nodal profile for first order quasilinear hyperbolic systems abstract for 1 d first order quasilinear hyperbolic systems without zero eigenvalues based on the theory of semi global c 1 solution by means of the results on both the exact boundary controllability and the exact boundary controllability of nodal profile using an extension method the exact controllability of nodal profile can be obtained purely with the help of internal controls moreover using a perturbation method by adding suitable internal controls to the part of equations corresponding to zero eigenvalues the corresponding exact internal controllability of nodal profile for 1 d first order quasilinear hyperbolic systems with zero eigenvalues can be also obtained

controllability for a scalar conservation law with nonlocal velocity abstract in this paper we study the state controllability and nodal profile controllability for a scalar conservation law with a nonlocal velocity that models a highly re entrant manufacturing system as encountered in semi conductor production we first prove a local state controllability result i e there exists a control that drives the solution from any given initial data to any desired final data in a certain time period provided that the initial and final data are both close to a given equilibrium 0 we also obtain a global state controllability result for the same system where there is no limitation on the distance between the initial and final data finally we prove a nodal profile controllability result i e there exists a control under which the solution starts from any initial data reaches exactly any given out flux over a fixed time period

boundary feedback stabilization of a class of coupled hyperbolic equations with nonlocal terms this paper solves the problem of boundary feedback stabilization of a class of coupled ordinary differential equations hyperbolic equations with boundary trace and integral nonlocal terms using the backstepping approach the controller is designed by formulating an integral operator whose kernel is required to satisfy a coupled hyperbolic partial integral differential equation by applying the method of successive approximations the kernel s well posedness is given we prove the exponential stability of the origin of the system in a suitable hilbert space moreover a wave system with nonlocal terms is stabilized by applying the above result

some results on the controllability of coupled semilinear wave equations the desensitizing control case first we consider a semilinear hyperbolic equation with partially known initial data in a bounded domain for this system we construct a locally distributed control that desensitizes a certain norm of the state this result is new and the method for proving it combines a judicious application of the carleman estimate and a localization technique then we discuss possible extensions of our result finally we apply our method to the exact controllability of two hyperbolic equations one semilinear and the other one linear coupled in cascade through the boundary the control acting in one equation only

internal controllability of first order quasi linear hyperbolic systems with a reduced number of controls in this paper we investigate the exact controllability of n times n first order one dimensional quasi linear hyperbolic systems by m n internal controls that are localized in space in some part of the domain we distinguish two situations the first one is when the equations of the system have the same speed in this case we can use the method of characteristics and obtain a simple and complete characterization for linear systems thanks to a linear test this also provides some sufficient conditions for the local exact controllability around the trajectories of semilinear systems however when the speed of the equations is not the same we see that we encounter the problem of loss of derivatives if we try to control quasi linear systems with a reduced number of controls to solve this problem as in a prior article by coron and lissy on a navier stokes control system we first use the notion of algebraic solvability due to gromov however in contrast with this prior article where a standard fixed

local exact controllability for the one dimensional compressible navier stokes equation in this paper we deal with the isentropic compressible navier stokes equation in one space dimension and we adress the problem of the boundary controllability for this system we prove that we can drive initial conditions which are sufficiently close to some constant states to those constant states this is done under some natural hypotheses on the time of control and on the regularity on the initial conditions

calderon zygmund type estimates for a class of obstacle problems with p x growth for local minimizers u wloc1 p of quasiconvex integral functionals of the type f u f x du x dx with p x growth in the class k u wloc1 p u where wloc1 p is a given obstacle function we show estimates of calderon zygmund type i e d p llocq du p llocq for any q 1 provided that the modulus of continuity of the exponent function p satisfies the condition log1 0as 0

exact boundary controllability for quasi linear hyperbolic systems using a result on the existence and uniqueness of the semiglobal c1 solution to the mixed initial boundary value problem for first order quasi linear hyperbolic systems with general nonlinear boundary conditions we establish the exact boundary controllability for quasi linear hyperbolic systems if the c1 norm of initial and final states is small enough

on the boundary control of systems of conservation laws this paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws we prove a general result on the asymptotic stabilization of a system near a constant state on the other hand we give an example showing that exact controllability in finite time cannot be achieved in general