a new phenomenon in the critical exponent for structurally damped semi linear evolution equations abstract in this paper we find the critical exponent for global small data solutions to the cauchy problem in r n for dissipative evolution equations with power nonlinearities u p or u t p u t t u t u u p u t p here n 0 with 2 we show that the critical exponent for each of the two nonlinearities is related to each of the two possible asymptotic profiles of the linear part of the equation which are described by the diffusion equations v t v 0 w t w 0 the nonexistence of global solutions in the critical and subcritical cases is proved by using the test function method under suitable sign assumptions on the initial data and lifespan estimates are obtained by assuming small initial data in sobolev spaces we prove the existence of global solutions in the supercritical case up to some maximum space dimension n and we derive l q estimates for the solution for q 1 for 2 the result holds in any space dimension n 1 the existence result also remains valid if and or are fractional

the critical exponent for the dissipative plate equation with power nonlinearity abstract in this paper we find the critical exponent of global small data solutions for a damped plate equation with power nonlinearity u t t u t t 2 u u t u p t 0 x r 2 and for a system of two weakly coupled damped plate equations we show how assuming small data in the energy space h 2 h 1 and in l 1 is sufficient to compensate the regularity loss type decay effect created by the rotational inertia term u t t

nonlinear scattering theory at low energy abstract we study the scattering theory of a conservative nonlinear one parameter group of operators on a hilbert space x relative to a group of linear unitary operators under certain hypotheses the scattering operator carries a neighborhood of 0 in x into x the theory is designed to apply to the semilinear schrodinger and klein gordon equations

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

tracking fixed point dynamics in an electrochemical system using delayed feedback control we report numerical and experimental results indicating successful tracking of stabilized fixed points solutions in an electrochemical system by applying a continuous delayed feedback technique periodic oscillations are suppressed via stabilization of a steady state fixed point subsequently using a simple continuation method involving an update term this stabilized fixed point is tracked through the bifurcation diagram as a system parameter is slowly varied under the influence of this tracking protocol inception of oscillatory dynamics is precluded over large parameter domains and through bifurcations

critical exponent for nonlinear wave equations with frictional and viscoelastic damping terms abstract in this paper we study the cauchy problem for a nonlinear wave equation with frictional and viscoelastic damping terms our aim is to obtain the threshold to classify the global existence of solutions for small initial data or the finite time blow up of solutions under the growth condition of the nonlinearity

global existence of small data solutions for wave models with super exponential propagation speed abstract we consider semi linear classical damped wave models with time dependent speed of propagation and time dependent dissipation the right hand side is a power nonlinearity which can be interpreted only as a source term we are interested in the interplay of time dependent coefficients on the global existence of small data solutions the considerations are divided into two cases depending on the behavior of the propagation speed the super exponential and the sub exponential case in this paper we study the super exponential case one main tool of our approach is the use of matsumura type estimates for a family of cauchy problems depending on a parameter

weighted strichartz estimates and global existence for semilinear wave equations in this paper we prove a sharp global existence theorem in all dimensions for nonlinear wave equations with power type nonlinearities the proof is based on a weighted strichartz estimate involving powers of the lorentz distance

long time asymptotic expansion for the damped semilinear wave equation the first initial boundary value problem is considered for the damped semilinear wave equation with the quadratic nonlinearity for small initial data and homogeneous boundary conditions its solution is constructed in the form of a series in the eigenfunctions of the laplace operator the long time asymptotic expansion is obtained which shows the nonlinear effects of amplitude and frequency multiplication the same results hold for the admissible initial data that are not small

on the existence and nonexistence of global solutions for certain semilinear exterior problems with nontrivial robin boundary conditions abstract we consider three types of semilinear equations elliptic parabolic and hyperbolic posed in the n dimensional exterior domain r n d where n 2 and d is the closed unit ball in r n a nontrivial robin boundary condition is imposed on the boundary of d using a test function approach with judicious choices of the test functions we show that the considered problems share a common critical behavior we discuss separately the cases n 2 and n 3 moreover in the case n 3 the dependence of the critical exponent on initial data is discussed to the best our knowledge the study of the critical behavior in an exterior domain with a nontrivial robin boundary condition has never been studied in the literature

weighted l2 estimates for dissipative wave equations with variable coefficients abstract we establish weighted l 2 estimates for the wave equation with variable damping u t t u a u t 0 in r n where a x a 0 1 x with a 0 0 and 0 1 in particular we show that the energy of solutions decays at a polynomial rate t n 2 1 if a x a 0 x for large x we derive these results by strengthening significantly the multiplier method this approach can be adapted to other hyperbolic equations with damping

decay of solutions for a semilinear system of elastic waves in an exterior domain with damping near infinity abstract we show that the solutions of a semilinear system of elastic waves in an exterior domain with a localized damping near infinity decay in an algebraic rate to zero we impose an additional condition on the lame coefficients it seems that this restriction cannot be overcome by using the two finite speed propagation of the elastic model since we do not assume compact support on the initial data and because the dissipation does not have compact support the decay rates obtained for the total energy of the linear problem and the l 2 norm of the solution improve previous results for the semilinear problem the decay rates in this paper seem to be the first contribution mainly in the context of initial data without compact support and localized dissipation

nonexistence of global solutions to semilinear wave equations in high dimensions on considere le probleme de cauchy pour l equation d onde semi lineaire 2 t 2 u x t u x t p p 1 u x o f x u t x o g x avec f g c o r n

brief paper multipliers for model predictive control with structured input constraints the stability and robustness of input constrained model predictive control can be analyzed using the theory of integral quadratic constraints we demonstrate the existence of improved multipliers when there are only staged input or box input constraints this can significantly reduce the conservatism of any stability analysis and we illustrate the improved performance with a simple numerical example

asymptotic behaviour of solutions for the wave equation with an effective dissipation around the boundary abstract we consider the initial boundary value problem for the wave equation with a dissipation a t x u t in an exterior domain whose boundary meets no geometrical condition we assume that the dissipation a t x u t is effective around the boundary and a t x decays as x we shall prove that the total energy does not in general decay and the solution is asymptotically free as the time goes to infinity further we shall show that the local energy decays like o t 1 t

global existence of weak solutions for two dimensional semilinear wave equations with strong damping in an exterior domain abstract we consider two dimensional mixed problems in an exterior domain for a semilinear strongly damped wave equation with a power type nonlinearity u p if the initial data have a small weighted energy we shall derive a global existence and energy decay results in the case when the power p of the nonlinear term satisfies p 6

bifurcation to large period oscillations in physical systems controlled by delay an unusual bifurcation to time periodic oscillations of a class of delay differential equations is investigated as we approach the bifurcation point both the amplitude and the frequency of the oscillations go to zero the class of delay differential equations is a nonlinear extension of a nonevasive control method and is motivated by a recent study of the foreign exchange rate oscillations by using asymptotic methods we determine the bifurcation scaling laws for the amplitude and the period of the oscillations

nonexistence of global solutions to a hyperbolic equation with a space time fractional damping we establish conditions that ensure the absence of global solutions to the nonlinear hyperbolic equation with a time space fractional damping u t email protected email protected b 2d au u p where email protected b 2 1 b 2 stands for the b 2 fractional power of the laplacien and d a is the riemann liouville s time fractional derivative 10 our results include nonexistence results as well as necessary conditions for the local and global solvability the method used is based on a duality argument with an appropriate choice of the test function and a scaling argument

orthogonal functions for cross directional control of web forming processes the cross directional behaviour of web forming processes can be represented in terms of orthogonal basis functions by choosing a suitable basis set it is possible to separate controllable and uncontrollable components of the profile into low and high order spectral components and hence obtain a parsimonious representation in most cases if there are sufficient actuators to control all low order spectral components then the interaction matrix is likely to be ill conditioned which necessitates the incorporation of input constraints into the control design the representation in terms of orthogonal functions allows the design of finite horizon predictive controllers with hard inequality constraints on the input that are computationally feasible for commercial machines it is also possible to exploit such a representation to construct efficient estimators for the process

nonexistence of global solutions for a time fractional damped wave equation in a k times halved space abstract in this paper we study the time fractional damped wave equation c d 0 u u c d 0 u u p t 0 x d k where 1 2 0 1 c d 0 is the left sided caputo fractional derivative of order with respect to the variable time t p 1 and d k k 1 2 n is the k times halved space given by d k x x 1 x 2 x n r n x i 0 i 1 2 k using the nonlinear capacity method we prove that the problem admits no global weak solutions with suitable initial data when 1 p 1 2 n k 2 1

new blow up results for nonlinear boundary value problems in exterior domains abstract we consider exterior boundary value problems with nontrivial boundary conditions including three types of semilinear equations heat equation wave equation and damped wave equation using a test function approach with a choice of a suitable family of test functions we obtain the critical exponents in the sense of fujita for the considered problems our obtained results close some open questions from the literature

diffusion phenomena for the wave equation with space dependent damping in an exterior domain abstract in this paper we consider the asymptotic behavior of solutions to the wave equation with space dependent damping in an exterior domain we prove that when the damping is effective the solution is approximated by that of the corresponding heat equation as time tends to infinity our proof is based on semigroup estimates for the corresponding heat equation and weighted energy estimates for the damped wave equation the optimality of the decay late for solutions is also established

diffusion phenomenon in hilbert spaces and applications abstract we prove an abstract version of the striking diffusion phenomenon that offers a strong connection between the asymptotic behavior of abstract parabolic and dissipative hyperbolic equations an important aspect of our approach is that we use in a natural way spectral analysis without involving complicated resolvent estimates our proof of the diffusion phenomenon does not use the individual behavior of solutions instead we show that only their difference matters we estimate the hilbert norm of the difference in terms of the hilbert norm of solutions to the parabolic problems which allows us to transfer the decay from the parabolic to the hyperbolic problem the application of these estimates to operators with markov property combined with a weighted nash inequality yields explicit and sharp decay rates for hyperbolic problems with variable x dependent coefficients in exterior domains our method provides new insight in this area of extensive research which was not well understood until now

strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation the aim of this article is twofold first we consider the wave equation in the hyperbolic space hi and obtain the counterparts of the strichartz type estimates in this context next we examine the relationship between semilinear hyperbolic equations in the minkowski space and in the hyperbolic space this leads to a simple proof of the recent result of georgiev lindblad and sogge on global existence for solutions to semilinear hyperbolic problems with small data shifting the space time strichartz estimates from the hyperbolic space to the minkowski space yields weighted strichartz estimates in rn x 1r which extend the ones of georgiev lindblad and sogge

improved decay rates for solutions to one dimensional linear and semilinear dissipative wave equations in all space abstract better decay estimates to the 1 dimensional cauchy problem on r to the linear equation u u t 0 can be discussed under rather restricted conditions on the initial data furthermore as applications we derive the small data global existence result to the equation u u t u p 1 u which has the odd functions as the initial data furthermore the new method see r ikehata t matsuyama sci math japon 55 2002 33 42 used in the first half will be applied to the problem coming from ehrenpreis sugaku 26 1974 168

critical exponents for nonlinear diffusion equations with nonlinear boundary sources abstract this paper is concerned with the large time behavior of solutions to two types of nonlinear diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball we are interested in the critical global exponent q 0 and the critical fujita exponent q c for the problems considered and show that q 0 q c for the multi dimensional porous medium equation and non newtonian filtration equation with nonlinear boundary sources this is quite different from the known results that q 0 q c for the one dimensional case

remark on the blow up of solutions for the semilinear wave equation with overdamping term abstract we consider the cauchy problem for the wave equation with overdamping and semilinear source terms p u t t u b t u t n u t x r r n u u t 0 x u 0 u 1 x x r n with b t b 0 t 1 b 0 0 1 and n u u p 1 u p 1 ikeda and wakasugi 8 have recently showed that when n u c u p for any p 1 there is a global in time solution to p for suitable small data and that when n u u p the local in time solution blows up within a finite time for suitable large data to show the blow up result their method seems to be not applicable to our semilinear term our aim is to show the blow up of solutions for suitable large data by the method much different from theirs

large time behavior and lp lq estimate of solutions of 2 dimensional nonlinear damped wave equations abstract we show the asymptotic behavior of the solution to the cauchy problem of the two dimensional damped wave equation it is shown that the solution of the linear damped wave equation asymptotically decompose into a solution of the heat and wave equations and the difference of those solutions satisfies the lp lq type estimate this is a two dimensional generalization of the three dimensional result due to nishihara math z 244 2003 631 to show this we use the fourier transform and observe that the evolution operators of the damped wave equation can be approximated by the solutions of the heat and wave equations by using the lp lq estimate we also discuss the asymptotic behavior of the semilinear problem of the damped wave equation with the power nonlinearity u u our result covers the whole super critical case 1 where the 1 is well known as the fujita exponent when n 2

asymptotic stability for nonlinear damped kirchhoff systems involving the fractional p laplacian operator abstract this paper is devoted to the question of global and local asymptotic stability for nonlinear damped kirchhoff systems with homogeneous dirichlet boundary conditions under fairly natural assumptions on the external force f f t x u the distributed damping q q t x u u t the perturbation term u p 2 u and the dissipative term t m u s p u t p 2 u t with 0 and in l loc 1 r 0 when the initial data are in a special region here u u 1 u n u t x represents the vectorial displacement with n 1 particular attention is devoted to the asymptotic behavior of the solutions in the linear case specified in section 5 finally the results are extended to problems where the fractional p laplacian is replaced by a more general elliptic nonlocal integro differential operator the paper extends in several directions recent theorems and covers also the so called degenerate case that is the case in which m is zero at zero

delayed feedback control of collective synchrony an approach to suppression of pathological brain rhythms we suggest a method for suppression of synchrony in a globally coupled oscillator network based on the time delayed feedback via the mean field having in mind possible applications for suppression of pathological rhythms in neural ensembles we present numerical results for different models of coupled bursting neurons a theory is developed based on the consideration of the synchronization transition as a hopf bifurcation

remarks on the asymptotic behavior of the solution to damped wave equations abstract we study the diffusion phenomena for damped wave equations we prove that the solution of an abstract damped wave equation becomes closer to the solution of a heat type equation as time tends to infinity under some assumption to the resolvent as an application of our approach we also study the asymptotic behavior of the damped wave equation in euclidean space under the geometric control condition

the diffusion phenomenon for dissipative wave equations in metric measure spaces abstract we study the long time behavior of the solution to a type of dissipative wave equation where the operator in the equation is time dependent and the solution is defined on a metric measure space x m satisfying appropriate conditions the operator is assumed to be self adjoint and is related to a time dependent dirichlet form we link hyperbolic pdes with the firmly established theories for parabolic pdes in metric measure spaces and dirichlet forms subsequently deriving the asymptotic behavior of the solution to the dissipative wave equation we present several nontrivial examples of dissipative wave equations in metric measure spaces where our theory works

adaptive cross direction control of paper basis weight abstract the initial setting and maintaining of the desired paper basis weight in machine direction and cross direction is to be ensured adaptively for several given paper grades technical equipment includes usual traversing gauge at the output of the paper machine special traversing robot for shaping the headbox lip sequential setting of screws control computer adaptive multivariate lqg control with recursive identification generalized to distributed parameter system has been designed with the following features integral convolution type model of the process respecting the continuous nature of all signals and kernels involved by means of spline approximation repetitive control synthesis via riccati equation with periodical solutions