on the controllability of some equations of sobolev galpern type abstract in this paper we deal with the controllability problem for some sobolev type equations we show that the equations cannot be driven to zero if the control region is strictly supported within the domain nevertheless we also prove that it is possible to control the equations using controls which have a moving support under some assumptions on their movement

stabilization of a boussinesq system of kdv kdv type a family of boussinesq systems has recently been proposed by bona chen and saut in j l bona m chen j c saut boussinesq equations and other systems for small amplitude long waves in nonlinear dispersive media i derivation and linear theory j nonlinear sci 12 4 2002 283 318 to describe the two way propagation of small amplitude gravity waves on the surface of water in a canal in this paper we investigate the boundary stabilization of the boussinesq system of kdv kdv type posed on a bounded domain we design a two parameter family of feedback laws for which the solutions issuing from small data are globally defined and exponentially decreasing in the energy space

on the controllability of the improved boussinesq equation the improved boussinesq equation is studied in this paper control properties for this equation posed on a bounded interval are first considered when the control acts through the dirichlet boundary condition the linearized system is proved to be approximately but not spectrally controllable in a second part the equation is posed on the one dimensional torus and distributed moving controls are considered under some condition on the velocity at which the control moves exact controllability results for both linear and nonlinear improved boussinesq equations are obtained applying the moment method and a fixed point argument

approximate controllability for linearized compressible barotropic navier stokes system in one and two dimensions abstract in this paper we consider compressible barotropic navier stokes equations in one and two dimensions linearized around a constant steady state with dirichlet boundary conditions we explore the controllability of this linearized system using a control only for the velocity equation we prove that the system with homogeneous dirichlet boundary conditions is approximately controllable by a localized interior control when time is sufficiently large

mobile point controls versus locally distributed ones for the controllability of the semilinear parabolic equation it is well known now that a rather general semilinear parabolic equation with globally lipschitz nonlinear term is both approximately and exactly null controllable in l2 omega when governed in a bounded domain by the locally distributed controls in this paper we intend to show that in fact in one space dimension omega 0 1 the very same results can be achieved by employing em at most two mobile point controls with support on the curves properly selected within an arbitrary subdomain of qt 0 1 0 t we will show that such curves can be described by a certain differential inequality and the explicit examples are provided we also discuss some extensions of our main results to the superlinear terms and to the case of several dimensions

sufficient conditions for conservativity of quantum dynamical semigroups abstract we give sufficient conditions for the conservativity of a quantum dynamical semi group these conditions are expressed as upper bounds of quadratic forms

null controllability of the structurally damped wave equation with moving control we investigate the internal controllability of the wave equation with structural damping on the one dimensional torus we assume that the control is acting on a moving point or on a moving small interval with a constant velocity we prove that the null controllability holds in some suitable sobolev space and after a fixed positive time independent of the initial conditions

on the controllability of the linearized benjamin bona mahony equation we study the boundary controllability properties of the linearized benjamin bona mahony equation left begin array ll u t u xxt u x 0 x in 0 1 t 0 u t 0 0 u 1 t f t t 0 end array right we show that the equation is approximately controllable but not spectrally controllable no finite linear combination of eigenfunctions other than zero is controllable next we prove a finite controllability result and we estimate the norms of the controls needed in this case

null controllability properties of the wave equation with a second order memory term abstract we study the internal controllability of a wave equation with memory in the principal part defined on the one dimensional torus t r 2 z we assume that the control is acting on an open subset t t which is moving with a constant velocity c r 1 0 1 the main result of the paper shows that the equation is null controllable in a sufficiently large time t and for initial data belonging to suitable sobolev spaces its proof follows from a careful analysis of the spectrum associated with our problem and from the application of the classical moment method

direct integrals of strongly continuous operator semigroups abstract the goal of this article is to develop a theory for direct integrals of c 0 semigroups on hilbert spaces parallel to the recent approach by lachowicz and moszynski for direct sums of banach spaces diagonal operators and semigroups in it we deal with the existence and characterisation of semigroups asymptotic rates and questions of decomposability

revisit on partial solutions in the adomian decomposition method solving heat and wave equations the adomian decomposition method is considered in application to heat and wave equations the so called partial solution technique is used it is shown that the fundamental equation of the method is well defined only for certain types of boundary conditions in cases involving inhomogeneous boundary conditions improper results may be obtained by former method this paper presents a further insight into partial solutions in the decomposition method and the resolution of such cases

controllability of the linear one dimensional wave equation with inner moving forces we address the null inner controllability of the one dimensional wave equation with supports of the controls that may vary with respect to the time variable we consider theoretical and numerical aspects assuming a geometric optic condition on the support of the controls we first prove a generalized observability inequality for the homogeneous wave equation implying the controllability we then introduce and prove the well posedness of a mixed formulation that characterizes the controls of minimal square integrable norm a numerical approximation of this formulation based on a conformal space time finite element method is then presented several numerical experiments are finally reported

experimentation with two step adomian decomposition method to solve evolution models the two step adomian decomposition method tsadm is derived by separate the standard adomian decomposition method into two steps although the tsadm needs only a slight variation from the standard adomian decomposition method experimentation shows that the tsadm is also promising for systems of inhomogeneous differential and integral equations hyperbolic partial differential equations and singular initial value problems

analysis of a viscoelastic spring mass model in this paper we consider a linear wave equation with strong damping and dynamical boundary conditions as an alternative model for the classical spring mass damper ode our purpose is to compare analytically these two approaches to the same physical system we take a functional analysis point of view based on semigroup theory spectral perturbation analysis and dominant eigenvalues

null controllability of the linearized compressible navier stokes system in one dimension in this paper we consider the one dimensional compressible navier stokes equations linearized around a constant steady state q0 v0 q0 0 v0 0 with periodic boundary conditions in the interval i2 0 2 we explore the controllability of this linearized system using a control only for the velocity equation we prove that the linearized system with homogeneous periodic boundary conditions is null controllable in h 1 per i2 l 2 i2 by a localized interior control when time is sufficiently large where h 1 per i2 denotes the sobolev space of periodic functions with mean value zero we show null controllability of the system by proving an observability inequality with the help of two types of ingham inequality

a complex analytic approach to the problem of uniform controllability of a transport equation in the vanishing viscosity limit abstract we revisit a result by coron and guerrero stating that the one dimensional transport diffusion equation u t m u x e u x x 0 in 0 t 0 l controlled by the left dirichlet boundary value is zero controllable at a bounded cost as e 0 when t 4 3 l m if m 0 and when t 57 2 l m if m 0 by a completely different method relying on complex analysis we prove that this still holds when t 4 2 l m if m 0 and when t 6 1 l m if m 0

null controllability of a pseudo parabolic equation with moving control abstract in this paper we study the internal controllability of the pseudo parabolic equation on the one dimensional torus our control function is acting on a moving small interval with a constant velocity with this moving distributed control we obtain the system is null controllable for given data with certain regularity

unique continuation and control for the heat equation from an oscillating lower dimensional manifold we consider the linear heat equation with dirichlet boundary conditions in a bounded domain of r n n geq 1 and with a control acting on a lower dimensional time dependent manifold of dimension k leq n 1 we analyze the approximate controllability problem this problem is equivalent to a suitable uniqueness or unique continuation property of solutions of the heat equation without control more precisely it consists of proving that the unique solution of the dirichlet problem vanishing on the time dependent manifold is identically zero this uniqueness problem however does not fit in the class of classical cauchy problems and therefore the existing tools based on power series expansions carleman inequalities and doubling properties do not seem to apply we give sufficient conditions on the time dependent manifold for this uniqueness property to hold the techniques we employ combine the fourier series representation and the time analyticity of solutions and allow us to reduce the problem to a uniqueness question for the eigenfunctions of the laplacian we then apply well known results on the nodal sets of these eigenfunctions we also analyze the asymptotic behavior of the control when the time oscillation of the manifold supporting the control increases when the frequency of oscillation tends to infinity we prove that the controls converge to an approximate control for the same heat equation but on a manifold of dimension k 1 that is independent of time this is done under suitable time periodicity assumptions on the original manifold and confirms the fact that increasing time oscillations of the support of the control increases the efficiency of the control mechanism

a new computational method for laplace transforms by decomposition method in this paper adomian decomposition method is applied to develop a new computational method for laplace transforms some examples are provided to illustrate the simplicity and reliability of the new method

controllability and asymptotic stabilization of the camassa holm equation we investigate the problems of exact controllability and asymptotic stabilization of the camassa holm equation on the circle by means of a distributed control the results are global and in particular the control prevents the solution from blowing up

unique continuation property and control for the benjamin bona mahony equation on a periodic domain abstract we consider the benjamin bona mahony bbm equation on the one dimensional torus t r 2 z we prove a unique continuation property ucp for small data in h 1 t with nonnegative zero means next we extend the ucp to certain bbm like equations including the equal width wave equation and the kdv bbm equation applications to the stabilization of the above equations are given in particular we show that when an internal control acting on a moving interval is applied in the bbm equation then a semiglobal exponential stabilization can be derived in h s t for any s 1 furthermore we prove that the bbm equation with a moving control is also locally exactly controllable in h s t for any s 0 and globally exactly controllable in h s t for any s 1 in a sufficiently large time depending on the h s norms of the initial and terminal states

controllability results for the moore gibson thompson equation arising in nonlinear acoustics abstract we show that the moore gibson thomson equation t t t y t t y c 2 y b t y k t t y 2 t u is controlled by a force that is supported on an moving subset t of the domain satisfying a geometrical condition using the concept of approximately outer invertible map a generalized implicit function theorem and assuming that c 2 b 0 the local null controllability in the nonlinear case is established moreover the analysis of the critical value 0 for the linear equation is included

controllability for one dimensional nonlinear wave equations with degenerate damping abstract internal exact controllability for the nonlinear wave equation in one space dimension y t t y x x g y y t h is studied where g is a nonnegative function for the case lim sup s g s ln s we obtain the global exact controllability for the equation with dirichlet boundary condition the proof is based on the combination of fixed point arguments and explicit observability estimates for the linearized wave equation with a potential that depends on both x and t for the case g s s we only get a local exact controllability by means of banach fixed point theorem

on the structure of covariant dynamical semigroups abstract dynamical semigroups in b h without the norm continuity assumption are investigated by introducing the notion of form generator giving the mathematical expression for the idea of markovian master equation it is shown that any form generator on b h admits a standard representation and the non uniqueness of this representation is described the equations for the components of the standard representation of a covariant form generator are deduced in terms of low order cohomology of the symmetry group in particular noncommutative levy khinchin type formulae for the shift covariant form generators are obtained relations with previous works on characterisation of the unbounded generator of a dynamical semigroup are discussed

a distinctive sumudu treatment of trigonometric functions abstract the sumudu transform integral equation is solved by continuous integration by parts to obtain its definition for trigonometric functions the transform variable u is included as a factor in the argument of f t and summing the integrated coefficients evaluated at zero yields the image of trigonometric functions the obtained result is inverted to show the expansion of trigonometric functions as an infinite series maple graphs tables of extended sumudu properties and infinite series expansions of trigonometric functions sumudi images are given

null controllability of a system of linear thermoelasticity we consider a linear system of thermoelasticity in a compact c infin n dimensional connected riemannian manifold this system consists of a wave equation coupled to a heat equation when the boundary of the manifold is non empty dirichlet boundary conditions are considered we study the controllability properties of this system when the control acts in the hyperbolic equation and not in the parabolic one and has its support restricted to an open subset of the manifold we show that if the control time and the support of the control satisfy the geometric control condition for the wave equation this system of thermoelasticity is null controllable more precisely any finite energy solution can be driven to zero at the control time an analogous result is proved when the control acts on the parabolic equation finally when the manifold has no boundary the null controllability of the linear system of three dimensional thermoelastic ity is proved

generators of quantum markov semigroups quantum markov semigroups qmss originally arose in the study of the evolutions of irreversible open quantum systems mathematically they are a generalization of classical markov semigroups where the underlying function space is replaced by a non commutative operator algebra in the case when the qms is uniformly continuous theorems due to the works of lindblad commun math phys 48 119 130 1976 stinespring proc am math soc 6 211 216 1955 and kraus ann phys 64 311 335 1970 imply that the generator of the semigroup has the form l a n 1 vn avn ga ag where vn and g are elements of the underlying operator algebra in the present paper we investigate the form of the generators of qmss which are not necessarily uniformly continuous and act on the bounded operators of a hilbert space we prove that the generators of such semigroups have forms that reflect the results of lindblad and stinespring we also make some progress towards forms reflecting kraus result finally we look at