well posedness and ill posedness for a fifth order shallow water wave equation abstract in this paper we establish a new bilinear estimate in suitable bourgain spaces by using a fundamental estimate on dyadic blocks for the kawahara equation which was obtained by the k z multiplier norm method of tao 2001 2 then the local well posedness of the cauchy problem for a fifth order shallow water wave equation in h s r with s 5 4 is obtained by the fourier restriction norm method and some ill posedness in h s r with s 5 4 is derived from a general principle of bejenaru and tao

on global identifiability for arbitrary model parametrizations it is a fundamental problem of identification to be able even before the data have been analyzed to decide if all the free parameters of a model structure can be uniquely recovered from data this is the issue of global identifiability in this contribution we show how global identifiability for an arbitrary model structure basically with analytic non linearities can be analyzed using concepts and algorithms from differential algebra it is shown how the question of global structural identifiability is reduced to the question of whether the given model structure can be rearranged as a linear regression an explicit algorithm to test this is also given furthermore the question of persistent excitation for the input can also be tested explicitly is a similar fashion the algorithms involved are very well suited for implementation in computer algebra one such implementation is also described

global regularity of wave maps from r3 1 to surfaces we consider wave maps with smooth compactly supported initial data of small norm from r3 1 to certain 2 dimensional riemannian manifolds and show that they stay smooth globally in time our methods are based on the introduction of a global coulomb gauge as in 17 followed by a dynamic separation as in 8 we then rely on an adaptation of t tao s methods used in his recent breakthrough result 24

multilinear estimates for periodic kdv equations and applications we prove an endpoint multilinear estimate for the xs b spaces associated to the periodic airy equation as a consequence we obtain sharp local well posedness results for periodic generalized kdv equations as well as some global well posedness results below the energy norm

paper identifiability and distinguishability concepts in electrochemistry although the notions of structural identifiability and distinguishability are now well accepted in some domains of mathematical modeling such as econometrics biology and pharmacokinetics much remains to be done in others the relevance of these notions to the building of phenomenological models in electrochemistry is illustrated by considering the volmer heyrovsky reaction and three mechanisms for dissolution passivation it is shown that some classical methods for collecting data cannot ensure suitable identifiability and distinguishability properties in some cases simple modifications of the experimental procedure can remove these ambiguities in others one may resort to more recent techniques of investigation

global well posedness for the three dimensional simplified inertial ericksen leslie systems near equilibrium abstract we study a simplified inertial ericksen leslie system for the nematic liquid crystal flow which can be viewed as a system coupling navier stokes equations and wave map equations we prove the global existence of classical solution with initial data near equilibrium

construction of type ii blowup solutions for the 1 corotational energy supercritical wave maps abstract we consider the energy supercritical wave maps from r d into the d sphere s d with d 7 under an additional assumption of 1 corotational symmetry the problem reduces to the one dimensional semilinear wave equation t 2 u r 2 u d 1 r r u d 1 2 r 2 sin 2 u we construct for this equation a family of c solutions which blow up in finite time via concentration of the universal profile u r t q r t where q is the stationary solution of the equation and the speed is given by the quantized rates t c u t t l l n l d 1 2 the construction relies on two arguments the reduction of the problem to a finite dimensional one thanks to a robust universal energy method and modulation techniques developed by merle raphael and rodnianski 49 for the energy supercritical nonlinear schrodinger equation then we proceed by contradiction to solve the finite dimensional problem and conclude using the brouwer fixed point theorem

state isomorphism approach to global identifiability of nonlinear systems global deterministic identifiability of nonlinear systems is studied by constructing the family of local state isomorphisms that preserve the structure of the parametric system the method is simplified for homogeneous systems where such isomorphisms are shown to be linear thereby reducing the identifiability problem to solving a set of algebraic equations the known conditions for global identifiability in linear and bilinear systems are special cases of these results

temps d existence pour l equation de klein gordon semi lineaire a donnees petites periodiques we study lower bounds for the maximal time of existence t of a smooth solution to a semi linear klein gordon equation u u f u u with periodic cauchy data of small size if f vanishes at order r at 0 we prove that t c 2 if r 2 t c r 1 log r 3 if r 3 we construct examples showing the optimality of these results for convenient values of r

on the cauchy problem for the generalized shallow water wave equation abstract in this paper we mainly study the cauchy problem for the generalized shallow water wave equation in the sobolev space h s of lower order s using the crucial bilinear estimates in the fourier transform restriction spaces related to the shallow water wave equation we establish local well posedness in h s with any s 11 16

structural resolvent estimates and derivative nonlinear schrodinger equations a refinement of a uniform resolvent estimate is given and several smoothing estimates for schrodinger equations in the critical case are induced from it the relation between this resolvent estimate and a radiation condition is discussed as an application of critical smoothing estimates we show a global existence result for derivative nonlinear schrodinger equations

null structure and almost optimal local well posedness of the maxwell dirac system we uncover the full null structure of the maxwell dirac system in lorenz gauge this structure which cannot be seen in the individual compo nent equations but only when considering the system as a whole is expressed in terms of tri and quadrilinear integral forms with cancellations measured by the angles between spatial frequencies in the 3d case we prove frequency localized l 2 space time estimates for these integral forms at the scale invariant regularity up to a logarithmic loss hence we obtain almost optimal local well posedness of the system by iteration

almost optimal local well posedness for the 3 1 dimensional maxwell klein gordon equations this paper contains a detailed study of the local in time regularity properties of the maxwell klein gordon mkg equations the mkg equations represent a physical model for the interaction of a spin 0 particle sometimes referred to as a higgs or scalar field with the classical equations of electrodynamics i e maxwell s equations in terms of the calculus of variations the mkg system consists of the euler lagrange equations associated to the density l 4 f f 1 2 d d where f a a is the electro magnetic field associated to the set a of real valued potentials on the minkowski space d 1a is the corresponding covariant derivative with respect to those potentials and r c is a complex scalar field in terms of the field f the euler lagrange equations read f d 1a d d 0 1b

global well posedness of the kp i initial value problem in the energy space we prove that the kp i initial value problem begin cases partial tu partial x 3u partial x 1 partial y 2u partial x u 2 2 0 text on mathbb r 2 x y times mathbb r t u 0 phi end cases is globally well posed in the energy space mathbf e 1 mathbb r 2 big phi mathbb r 2 to mathbb r phi mathbf e 1 mathbb r 2 approx phi l 2 partial x phi l 2 big partial x 1 partial y phi big l 2 infty big

codimension one stability of the catenoid under the vanishing mean curvature flow in minkowski space we study timelike hypersurfaces with vanishing mean curvature in the 3 1 dimensional minkowski space which are the hyperbolic counterparts to minimal embeddings of riemannian manifolds the catenoid is a stationary solution of the associated cauchy problem this solution is linearly unstable and we show that this instability is the only obstruction to the global nonlinear stability of the catenoid more precisely we prove in a certain symmetry class the existence in the neighborhood of the catenoid initial data of a codimension one lipschitz manifold transverse to the unstable mode consisting of initial data whose solutions exist globally in time and converge asymptotically to the catenoid

global well posedness and inviscid limit for the korteweg de vries burgers equation abstract considering the cauchy problem for the korteweg de vries burgers equation u t u x x x x 2 u u 2 x 0 u 0 where 0 1 and u is a real valued function we show that it is globally well posed in h s s s and uniformly globally well posed in h s s 3 4 for all 0 1 moreover we prove that for any t 0 its solution converges in c 0 t h s to that of the kdv equation if tends to 0

sharp local well posedness for a fifth order shallow water wave equation abstract in this paper we prove that the already established local well posedness in the range s 5 4 of the cauchy problem with an initial h s r data for a fifth order shallow water wave equation is extendable to s 5 4 by using the f s space this is sharp in the sense that the ill posedness in the range s 5 4 of this initial value problem is already known

identifiabilty of systems described by convolution equations parameter identifiability is studied for a class of finite and infinite dimensional systems described by convolution equations the notion of sufficiently rich input which enforces identifiability is also addressed and the results are obtained assuming knowledge of solutions on a bounded time interval

absence of self similar blow up and local well posedness for the constant mean curvature wave equation abstract in this note we consider the constant mean curvature wave equation in 1 2 dimensions we show that it does not admit any self similar blow up we also remark that the equation is locally well posed for initial data in h 3 2

ill posedness for one dimensional wave maps at the critical regularity we show that the wave map equation in r 1 1 is in general ill posed in the critical space 1 2 and the besov space 1 2 1 2 the problem is attributed to the bad behavior of the one dimensional bilinear expression d 1 fdg in these spaces

on a model connected with the kirchhoff equation abstract we prove a global existence result in suitable sobolev spaces for the solution of the nonlinear cauchy problem tt u t x 1 r n dy k x y y u t y 2 x u t x 0 u 0 x u 0 x t u 0 x u 1 x 0 where n 3 is the space dimension the initial data are c with compact support in rn and k z is a positive smooth function rapidly decreasing as z our approach is based on the energy estimates combined with the classical von wahl inequalities

technical communique injectivity analysis using interval analysis application to structural identifiability this paper presents a new numerical algorithm based on interval analysis able to prove that a differentiable function f email protected r n r n is injective this algorithm also performs a partition of the domain a in subsets a i where for all email protected a i the cardinality of f 1 f x is constant in the context of parameter estimation we show how this algorithm provides an efficient and numerical method to study the structural identifiability of parametric models

sharp well posedness and ill posedness results for a quadratic non linear schrodinger equation abstract we establish that the quadratic non linear schrodinger equation iu t u xx u 2 where u r r c is locally well posed in h s r when s 1 and ill posed when s 1 previous work in c kenig g ponce l vega quadratic forms for the 1 d semilinear schrodinger equation trans amer math soc 346 1996 3323 3353 had established local well posedness for s 3 4 the local well posedness is achieved by an iteration using a modification of the standard x s b spaces the ill posedness uses an abstract and general argument relying on the high to low frequency cascade present in the non linearity and a computation of the first non linear iterate

a novel method to estimate the stiffness of the equine back diagnosis of back problems in equine orthopedics can be a difficult task the aim of our study was to develop a new method for estimating the stiffness of the equine back in vivo we measured the activity of the long back muscle at two locations on both sides at thoracic vertebrae t12 and t16 of 15 horses flexing and extending their back at stance using telemetric surface electromyography while simultaneously recording the motion of the back with a video camera system out of these paired data sets we computed a transfer function in the frequency domain and evaluated its capability of capturing the biomechanical behavior the transfer function was evaluated via correlation between calculated and actual motion resulting in correlation coefficients of 0 89 for lateral flexion and 0 83 for ventral extension at t16 and 0 82 for lateral flexion and 0 83 for ventral extension at t12 the transfer function was fitted to a filter polynomial of second order and related to the motion equation by comparison of coefficients we gained an estimate for the stiffness of the back resulting in a mean value of approximately 6100 n m for lateral flexion and 650 n m for ventral extension this new method enables clinicians in equine orthopedics to estimate back stiffness in horses and it also provides reality grounded values for biomechanical models of the equine back

automatic integration of euler lagrange equations with constraints abstract numerical difficulties in the integration of euler lagrange and similar equations are discussed a technique for reducing their index from three to two is introduced and it is shown that variable order variable step bdf methods converge for these index two problems the practical application of this reduction in a numerical setting is examined

simulation of quadrupedal locomotion using a rigid body model locomotion of the horse is simulated using a mathematical model based on rigid body dynamics a general method to generate the equations of motion for a two dimensional rigid body model with an arbitrary number of hinge joints is presented and a numerical solution method restricted to tree structured models is described joint movements originating from muscular forces or moments are simulated but the method also allows that parts of the model follow strictly the pattern of kinematic data moment generators with first order linear feedback were used as a rotational muscle equivalent ground hoof interaction forces are approximated by a viscoelastic model and pseudo coulomb friction in vertical and horizontal directions respectively results of model simulations are compared to experimentally recorded data subsequently adjustments are made to improve the agreement between simulation and experimental results

a comparison of muscle energy models for simulating human walking in three dimensions the popular hill model for muscle activation and contractile dynamics has been extended with several different formulations for predicting the metabolic energy expenditure of human muscle actions these extended models differ considerably in their approach to computing energy expenditure particularly in their treatment of active lengthening and eccentric work but their predictive abilities have never been compared in this study we compared the predictions of five different hill based muscle energy models in 3d forward dynamics simulations of normal human walking in a data tracking simulation that minimized muscle fatigue the energy models predicted metabolic costs that varied over a three fold range 2 45 7 15 j m kg with the distinction arising from whether or not eccentric work was subtracted from the net heat rate in the calculation of the muscle metabolic rate in predictive simulations that optimized neuromuscular control to minimize the metabolic cost all five models predicted similar speeds step lengths and stance phase durations however some of the models predicted a hip circumduction strategy to minimize metabolic cost while others did not and the accuracy of the predicted knee and ankle angles and ground reaction forces also depended on the energy model used the results highlights the need to clarify how eccentric work should be treated when calculating muscle energy expenditure the difficulty in predicting realistic metabolic costs in simulated walking even with a detailed 3d musculoskeletal model the potential for using such models to predict energetically optimal gait modifications and the room for improvement in existing muscle energy models and locomotion simulation frameworks

decay estimates for a class of wave equations abstract in this paper we use a unified way studying the decay estimate for a class of dispersive semigroup given by e i t where r r is smooth away from the origin especially the decay estimates for the solutions of the klein gordon equation and the beam equation are simplified and slightly improved

multilinear weighted convolution of l 2 functions and applications to nonlinear dispersive equations the x s b spaces as used by beals bourgain kenig ponce vega klainerman machedon and others are fundamental tools to study the low regularity behavior of nonlinear dispersive equations it is of particular interest to obtain bilinear or multilinear estimates involving these spaces by plancherel s theorem and duality these estimates reduce to estimating a weighted convolution integral in terms of the l 2 norms of the component functions in this paper we systematically study weighted convolution estimates on l 2 as a consequence we obtain sharp bilinear estimates for the kdv wave and schrodinger x s b spaces

on the cauchy problem for the zakharov system abstract we study the local cauchy problem in time for the zakharov system 1 1 and 1 2 governing langmuir turbulence with initial data u 0 n 0 t n 0 h k h lscr h l 1 in arbitrary space dimension we define a natural notion of criticality according to which the critical values of k l are 2 3 2 2 2 using a method recently developed by bourgain we prove that the zakharov system is locally well posed for a variety of values of k l the results cover the whole subcritical range for 4 for 3 they cover only part of it and the lowest admissible values are k l 1 2 0 for 2 3 and k l 0 1 2 for 1 as a by product of the one dimensional result we prove well posedness of the benney system 1 14 and 1 15 governing the interaction of short and long waves for the same values of k l

equations d ondes quasilineaires et estimations de strichartz dans cet article notre but est de resoudre des equations d ondes quasilineaires pour des donnees initiales moins regulieres que ce qu imposent les methodes d energie ceci impose de demontrer des estimees de type strichartz pour des operateurs d ondes a coefficients seulement lipschitziens

global well posedness of the maxwell dirac system in two space dimensions in recent work grunrock and pecher proved that the dirac klein gordon system in 2d is globally well posed in the charge class data in l 2 for the spinor and in a suitable sobolev space for the scalar field here we obtain the analogous result for the full maxwell dirac system in 2d making use of the null structure of the system found in earlier joint work with damiano foschi we first prove local well posedness in the charge class to extend the solutions globally we build on an idea due to colliander holmer and tzirakis for this we rely on the fact that md is charge subcritical in two space dimensions and make use of the null structure of the maxwell part

predictions of knee and ankle moments of force in walking from emg and kinematic data abstract a deterministic model was developed and validated to calculate instantaneous ankle and knee moments during walking using processed emg from representative muscles instantaneous joint angle as a correlate of muscle length and angular velocity as a correlate of muscle velocity and having available total instantaneous joint moments for derivation of certain model parameters a linear regression of the moment on specifically processed emg recorded while each subject performed cycled isometric calibration contractions yielded the constants for a basic moment emg relationship using the resultant moment for optimization the predicted moment was proportionally augmented for longer muscle lengths and reduced for shorter lengths similarly the predicted moment was reduced for shortening velocities and increased if the muscle was lengthening the plots of moments predicted using the full model and those calculated from link segment mechanics followed each other quite closely the range of root mean square errors were 3 2 9 5 nm for the ankle and 4 7 13 0 nm for the knee

global regularity of wave maps from r 2 1 to h 2 small energy we demonstrate that wave maps with smooth initial data and small energy from r2 1 to the lobatchevsky plane stay smooth globally in time our method is similar to the one employed in 18 however the multilinear estimates required are considerably more involved and present novel technical challenges in particular we shall have to work with a modification of the functional analytic framework used in 30 33 18

on the structural output distinguishability of parametric models and its relations with structural identifiability in this note the notion of output distinguishability is extended to parametric models with different structures methods are suggested for testing such models for structural output distinguishability the possible relations of structural output distinguishability with structural identifiability and other structural properties are investigated

well posedness of the initial value problem for the korteweg de vries equation 1 1 itu axu u1xu o x t e r u x 0 uo x the kdv equation which was first derived as a model for unidirectional propagation of nonlinear dispersive long waves 21 has been considered in different contexts namely in its relation with the inverse scattering method in plasma physics and in algebraic geometry see 24 and references therein our purpose is to study local and global well posedness of the ivp 1 1 in classical sobolev spaces hs r we shall say that the ivp 1 1 is locally resp globally well posed in the function space x if it induces a dynamical system on x by generating a continuous local resp global flow it was established in the works of bona and smith 3 bona and scott 2 saut and temam 30 and kato 1 5 that the ivp 1 1 is locally resp globally well posed in hs with s 3 2 resp s 2 roughly speaking global well posedness in hs depends on the available local theory and on the conservation laws satisfied by solutions of 1 1 namely

quadratic forms for the 1 d semilinear schrodinger equation this paper is concerned with 1 d quadratic semilinear schr6dinger equations we study local well posedness in classical sobolev space hs of the associated initial value problem and periodic boundary value problem our main interest is to obtain the lowest value of s which guarantees the desired local well posedness result we prove that at least for the quadratic cases these values are negative and depend on the structure of the nonlinearity considered

global solutions of the klein gordon schrodinger system with rough data in r 2 1 abstract in this paper we consider the klein gordon schrodinger system with quadratic yakuwa coupling and cubic autointeractions in r 2 1 and prove the existence and uniqueness of global solution for rough data the techniques to be used are adapted from a general scheme originally introduced by j bourgain to split the data into the low and high frequency parts

a bilinear estimate with applications to the kdv equation u x 0 u0 x where u0 h r our principal aim here is to lower the best index s for which one has local well posedness in h r i e existence uniqueness persistence and continuous dependence on the data for a finite time interval whose size depends on u0 hs equation in 1 1 was derived by korteweg and de vries 21 as a model for long wave propagating in a channel a large amount of work has been devoted to the existence problem for the ivp 1 1 for instance see 9 10 the inverse scattering method applies to this problem and under appropriate decay assumptions on the data several existence results have been established see 5 6 14 28 33 another approach inherited from hyperbolic problems relies on the energy estimates and in particular shows that 1 1 is locally well posed in h r for s 3 2 see 2 3 12 29 30 31 using these results and conservation laws global in time well posedness in h r s 2 was established see 3 12 30 also global in time weak solutions in the energy space h r were constructed in 34 in 13 and 22 a local smoothing effect for solutions of 1 1 was discovered this combined with the conservation laws was used in 13 and 22 to construct global in time weak solutions with data in h r and even in l r in 16 we introduced oscillatory integral techniques to establish local well posedness of 1 1 in h r s 3 4 and hence global in time well posedness in h r s 1 in 16 we showed how to obtain the above mentioned result by picard iteration in an appropriate function space in 4 j bourgain introduced new function spaces adapted to the linear operator t 3 x for which there are good bilinear estimates for the nonlinear term x u 2 using these spaces bourgain was able to establish local well posedness of 1 1 in h r l r and hence by a conservation