hs global well posedness for semilinear wave equations abstract we consider the cauchy problem for semilinear wave equations in r n with n 3 making use of bourgain s method in conjunction with the endpoint strichartz estimates of keel and tao we establish the hs global well posedness with s

generalized strichartz estimates and scattering for 3d zakharov system we obtain scattering for the 3d zakharov system with non radial small data in the energy space with angular regularity of degree one the main ingredient is a generalized strichartz estimate for the schrodinger equation in the space of l2 angular integrability

strichartz estimates in similarity coordinates and stable blowup for the critical wave equation we establish strichartz estimates in similarity coordinates for the radial wave equation in three spatial dimensions with a time dependent self similar potential as an application we consider the critical wave equation and prove the asymptotic stability of the ode blowup profile in the energy space

propagation de l analyticite des solutions de systemes hyperboliques non lineaires on montre que si l on se place dans un domaine ou la solution est a priori assez reguliere la regularite analytique s etend des donnees de cauchy a la solution selon la geometrie des domaines d influence de l equation comme dans le cas lineaire en particulier si les donnees de cauchy sont analytiques une solution est analytique jusqu au premier choc

regularity and decay of solutions of nonlinear harmonic oscillators abstract we prove sharp analytic regularity and decay at infinity of solutions of variable coefficients nonlinear harmonic oscillators namely we show holomorphic extension to a sector in the complex domain with a corresponding gaussian decay according to the basic properties of the hermite functions in r d our results apply in particular to nonlinear eigenvalue problems for the harmonic oscillator associated to a real analytic scattering or asymptotically conic metric in r d as well as to certain perturbations of the classical harmonic oscillator

local cauchy problem for the nonlinear dirac and dirac klein gordon equations on kerr space time we prove the local existence of solutions of nonlinear dirac and dirac klein gordon equations in kerr metric with regular cauchy initial datas

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

gauss jacobi quadratures for weakly strongly hyper and nearly singular integrals in boundary integral equation methods for domains with sharp edges and corners abstract we present gauss jacobi quadrature rules in terms of hypergeometric functions for the discretization of weakly singular strongly singular hypersingular and nearly singular integrals that arise in integral equation formulations of potential problems for domains with sharp edges and corners the rules are tailored to weight functions with algebraic endpoint singularities of a fairly general form thus allowing one to easily incorporate a wide class of domains into the analysis numerical examples illustrate the accuracy and stability of the proposed algorithms it is shown that the same level of high accuracy can be achieved for any choice of the external variable the usefulness of the method is exemplified by application to the solution of a singular integral equation that arises in time harmonic electromagnetic scattering by either closed or open perfectly conducting cylindrical objects with edges and corners such as polygon cylinders and bent strips some practical aspects concerning the role of nearby singularities in achieving a highly accurate solution of singular integral equations are also discussed

on the domain of analyticity of solutions to semilinear klein gordon equations abstract we consider initial value problems for semilinear klein gordon equations u t t x u u f u 0 with periodic boundary conditions assuming that both the initial data and the nonlinear forcing term f u are analytic we provide explicit lower bounds on the decay of the radius t of analyticity of the solutions as a function of time in particular in one space dimension with u real valued and f u u 2 k 1 we prove that the decay of t is not worse than 1 t the results are given in a general framework including gevrey class solutions

asymptotic error expansions and splitting extrapolation algorithm for two classes of two dimensional cauchy principal value integrals abstract this paper proposes numerical quadrature rules for two dimensional cauchy principal value integrals of the forms f x y x s 2 y t 2 d y d x and f x y x s y t d y d x the derivation of these quadrature rules is based on the euler maclaurin error expansion of a modified trapezoidal rule for one dimensional cauchy singular integrals the corresponding error estimations are investigated and the convergence rates o h m 2 h n 2 are obtained for the proposed quadrature rules where hm and hn are partition sizes in x and y directions is a positive integer determined by integrand to further improve accuracy a splitting extrapolation algorithm is developed based on the asymptotic error expansions several numerical tests are performed to verify the effectiveness of the proposed methods

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

nonlinear q design for convex stochastic control in this note we describe a version of the q design method that can be used to design nonlinear dynamic controllers for a discrete time linear time varying plant with convex cost and constraint functions and arbitrary disturbance distribution choosing a basis for the nonlinear q parameter yields a convex stochastic optimization problem which can be solved by standard methods such as sampling in principle for a large enough basis and enough sampling this method can solve the controller design problem to any degree of accuracy in any case it can be used to find a suboptimal controller using convex optimization methods we illustrate the method with a numerical example comparing a nonlinear controller found using our method with the optimal linear controller the certainty equivalent model predictive controller and a lower bound on achievable performance obtained by ignoring the causality constraint

an iterative learning control for a class of partially feedback linearizable systems a class of single input single output nonlinear systems which are partially linearizable by state feedback is considered feedback linearizable systems are included in such a class no parametrization is required for the uncertainties which are required to satisfy the matching condition periodic reference signals with known period t are to be tracked by the output provided that known bounding functions on the uncertainties are available a state feedback iterative learning control is designed which achieves asymptotic output tracking and guarantees bounded closed loop signals from any intial condition the novel control tecnhique is illustrated for a single link robot arm

endpoint bilinear restriction theorems for the cone and some sharp null form estimates recently wolff 25 obtained a nearly sharp l 2 bilinear restriction theorem for bounded subsets of the cone in general dimension we obtain the endpoint of wolff s estimate and generalize to the case when one of the subsets is large as a consequence we are able to deduce some nearly sharp l p null form estimates

analyticity and smoothing effect for the korteweg de vries equation with a single point singularity we show that a solution of the cauchy problem for the kdv equation cases partial tv partial 3 x v partial x v 2 0 qquad t in t t x in bbb r v 0 x phi x endcases has a drastic smoothing effect up to real analyticity if the initial data only have a single point singularity at x 0 it is shown that for h s mathbb r s 3 4 data satisfying the condition sum k 0 infty frac a 0 k k x partial x k phi h s infty the solution is analytic in both space and time variable the above condition allows us to take as initial data the dirac delta measure or the cauchy principal value of 1 x the argument is based on the recent progress on the well posedness result by bourgain 2 and kenig ponce vega 20 and a systematic use of the dilation generator 3t partial t x partial x

symmetric galerkin bem simulation of fracture with frictional contact a symmetric galerkin boundary element framework for fracture analysis with frictional contact crack friction on the crack surfaces is presented the algorithm employs a continuous interpolation on the crack surface utilizing quadratic boundary elements and enables the determination of two important quantities for the problem namely the local normal tractions and sliding displacements on the crack surfaces an effective iterative scheme for solving this non linear boundary value problem is proposed the results of test examples are compared with available analytical solutions or with those obtained from the displacement discontinuity method ddm using linear elements and internal collocation the results demonstrate that the method works well for difficult kinked junction crack problems copyright 2003 john wiley sons ltd

sharp null form estimates for the wave equation null form estimates from dot h alpha 1 times dot h alpha 2 to l q t l r x for the wave equation in bbb r n 1 are studied for n ge4 we obtain the sharp null form estimates except for the endpoints for n 2 3 we obtain the estimates under the additional assumption 4 n q when 2 r

some remarks on strichartz estimates for homogeneous wave equation abstract we give several remarks on strichartz estimates for homogeneous wave equation with special attention to the cases of l x estimates radial solutions and initial data from the inhomogeneous sobolev spaces in particular we give the failure of the endpoint estimate l t 4 l x for n 2

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

frictional contact problems of kinked cracks modelled by a boundary integral method a numerical method is presented for the solution of two dimensional crack problems including the effects of crack kinks and frictional contact between crack faces the method is based on an integral equation for the resultant forces along a crack coulomb friction between contacting crack surfaces is taken into account the numerical implementation is demonstrated by considerations of surface and sub surface piece wise straight line cracks in a half plane numerical results are presented to illustrate the efficiency and the reliability of the presented method

on the radius of spatial analyticity for semilinear symmetric hyperbolic systems abstract we study the problem of propagation of analytic regularity for semi linear symmetric hyperbolic systems we adopt a global perspective and we prove that if the initial datum extends to a holomorphic function in a strip of radius width e 0 the same happens for the solution u t for a certain radius e t as long as the solution exists our focus is on precise lower bounds on the spatial radius of analyticity e t as t grows we also get similar results for the schrodinger equation with a real analytic electromagnetic potential

nonsingular terminal sliding mode control of robot manipulators using fuzzy wavelet networks this paper presents an adaptive nonsingular terminal sliding mode ntsm tracking control design for robotic systems using fuzzy wavelet networks compared with linear hyperplane based sliding control terminal sliding mode controller can provide faster convergence and higher precision control therefore a terminal sliding controller combined with the fuzzy wavelet network which can accurately approximate unknown dynamics of robotic systems by using an adaptive learning algorithm is an attractive control approach for robots in addition the proposed learning algorithm can on line tune parameters of dilation and translation of fuzzy wavelet basis functions and hidden to output weights therefore a robust control law is used to eliminate uncertainties including the inevitable approximation errors resulted from the finite number of fuzzy wavelet basis functions the proposed controller requires no prior knowledge about the dynamics of the robot and no off line learning phase moreover both tracking performance and stability of the closed loop robotic system can be guaranteed by lyapunov theory finally the effectiveness of the fuzzy wavelet network based control approach is illustrated through comparative simulations on a six link robot manipulator

solving strongly singular integral equations by lp approximation methods it has previously been shown that integral equations can be solved effectively by means of an l p approximation technique and particularly by means of an l 1 approximation this method has also successfully been applied to singular integral equations in the present discussion attention is paid to solving strongly singular integral equations via l p approximation techniques and in particular to the case of integral equations containing hadamard or finite part integrals

solitary waves for the klein gordon dirac model abstract we study the existence of solitary waves for non autonomous klein gordon dirac equations with a subcritical nonlinear term via variational methods the problem is strongly indefinite and lacks compactness to overcome these difficulties we use the linking and concentration compactness arguments

the global cauchy problem for the non linear klein gordon equation on demontre l unicite de solutions faibles et l existence et l unicite de solutions globales fortement continues dans l espace energie

fractional derivative estimates in gevrey spaces global regularity and decay for solutions to semilinear equations in rn abstract we propose a unified functional analytic approach to study the uniform analytic gevrey regularity and the decay of solutions to semilinear elliptic equations on r n first we develop a fractional calculus for nonlinear maps in banach spaces of l p based gevrey functions 1 h p s r n regularity with s scr 0 depending on the nonlinearity next we investigate the type of decay polynomial or exponential of the derivatives of solutions to semilinear elliptic equations provided they decay a priori slowly as o x x for some small 0 the restrictions involved in our results are optimal in particular given a hyperplane l we construct 2d 2 strongly singular solutions locally in h p s r n for s

well posedness for a quadratic derivative nonlinear schrodinger system at the critical regularity abstract we consider the cauchy problem for a quadratic derivative nonlinear schrodinger system in sobolev space h s in this paper under the null condition and the mass resonance relation we prove large data local well posedness if the space dimension d 3 and s s c d 2 and s s c or d 1 and s 0 where s c is the scaling critical regularity moreover under the same assumptions we also prove small data global well posedness and scattering in h s if d 3 and s s c our proof is based on a contraction argument using the u p and v p type function spaces

remarks on the gauss quadrature rule for a particular class of finite part integrals the method of finite part hadamard type or hypersingular integrals is already a standard approach in applied numerical methods in engineering and mainly in acoustics fluid dynamics elasticity and fracture mechanics here we study the convergence of the non classical possessing a negative node outside the integration interval as well as a negative weight corresponding to this node gauss legendre quadrature rule for finite part integrals on the interval 0 1 with the weight function 1 y and we prove its validity for integrands possessing a continuous first derivative the case of integrands possessing a higher order derivative is also considered and the rate of convergence is established these results are based on the derivation of a bound for the negative node in the above quadrature rule and further on the theory of convergence of the classical gauss quadrature rule numerical results verifying the results of this paper are also displayed the present results can be generalized to the gauss laguerre similarly non classical quadrature rule for finite part integrals on the interval 0 as well as to the two special but important in engineering applications non classical gaussian quadrature rules for cauchy type principal value integrals and mangler type finite part integrals have been proposed by tsamasphyros and dimou

remarks on a weighted energy estimate and its application to nonlinear wave equations in one space dimension abstract a weighted energy estimate with tangential derivatives on the light cone is applied for the cauchy problem of semilinear wave equations with the null conditions in one space dimension the well posedness and lifespan of the solutions are considered based on the vector field method

a uniformly accurate multiscale time integrator spectral method for the kleingordonzakharov system in the high plasma frequency limit regime a multiscale time integrator sine pseudospectral mti sp method is presented for discretizing the kleingordonzakharov kgz system with a dimensionless parameter 0 1 which is inversely proportional to the plasma frequency in the high plasma frequency limit regime i e 0 1 the solution of the kgz system propagates waves with amplitude at o 1 and wavelength at o 2 in time and o 1 in space which causes significantly numerical burdens due to the high oscillation in time the main idea of the numerical method is to carry out a multiscale decomposition by frequency mdf to the electric field component of the solution at each time step and then apply the sine pseudospectral discretization for spatial derivatives followed by using the exponential wave integrator in phase space for integrating the mdf and the equation of the ion density component the method is explicit and easy to be implemented extensive numerical results show that the mti sp method converges uniformly and optimally in space with exponential convergence rate if the solution is smooth and uniformly in time with linear convergence rate at o for 0 1 with time step size and optimally with quadratic convergence rate at o 2 in the regime when either o 1 or 0 thus the meshing strategy requirement or scalability of the mti sp for the kgz system in the high plasma frequency limit regime is o 1 and h o 1 for 0 1 which is significantly better than classical methods in the literatures finally we apply the mti sp method to study the convergence rates of the kgz system to its limiting models in the high plasma frequency limit and the interactions of bright solitons of the kgz system and to identify certain parameter regimes that the solution of the kgz system will be blow up in one dimension

endpoint strichartz estimates for the magnetic schrodinger equation abstract we prove strichartz estimates for the schrodinger equation with an electromagnetic potential in dimension n 3 the decay and regularity assumptions on the potentials are almost critical i e close to the coulomb case in addition we require repulsivity and a nontrapping condition which are expressed as smallness of suitable components of the potentials while the potentials themselves can be large the proof is based on smoothing estimates and new sobolev embeddings for spaces associated to magnetic potentials

robust dynamic sliding mode control using adaptive renn for magnetic levitation system in this paper a robust dynamic sliding mode control system rdsmc using a recurrent elman neural network renn is proposed to control the position of a levitated object of a magnetic levitation system considering the uncertainties first a dynamic model of the magnetic levitation system is derived then a proportional integral derivative pid type sliding mode control system smc is adopted for tracking of the reference trajectories moreover a new pid type dynamic sliding mode control system dsmc is proposed to reduce the chattering phenomenon however due to the hardware being limited and the uncertainty bound being unknown of the switching function for the dsmc an rdsmc is proposed to improve the control performance and further increase the robustness of the magnetic levitation system in the rdsmc an renn estimator is used to estimate an unknown nonlinear function of lumped uncertainty online and replace the switching function in the hitting control of the dsmc directly the adaptive learning algorithms that trained the parameters of the renn online are derived using lyapunov stability theorem furthermore a robust compensator is proposed to confront the uncertainties including approximation error optimal parameter vectors and higher order terms in taylor series finally some experimental results of tracking the various periodic trajectories demonstrate the validity of the proposed rdsmc for practical applications

nonlinear integral type sliding surface for both matched and unmatched uncertain systems this note presents a new nonlinear integral type sliding surface which incorporates a virtual nonlinear nominal control to achieve prescribed specifications first the plant with matched uncertainties is considered the resultant closed loop system during ideal sliding mode behaves exactly like the nominal plant under the nonlinear nominal control which completely nullifies the matched uncertainties and consequently satisfies the prescribed specifications second the stability analysis of the proposed sliding mode for the systems with unmatched uncertainties is performed to exploit the stability conditions numerical results demonstrate the validity of the proposed concept

the wave maps equation the wave maps equation has become a very popular topic in recent years the aim of these expository notes is to present a non technical survey of the ideas and methods which have proved useful in the study of wave maps leading up to the latest results the remaining open problems are also stated and explained

low regularity global well posedness for the zakharov and klein gordon schrodinger systems we prove low regularity global well posedness for the id zakharov system and the 3d klein gordon schrodinger system which are systems in two variables u r d x x r t c and n r d x x r t r the zakharov system is known to be locally well posed in u n l 2 x h and the klein gordon schrodinger system is known to be locally well posed in u n l 2 x l 2 here we show that the zakharov and klein gordon schrodinger systems are globally well posed in these spaces respectively by using an available conservation law for the l 2 norm of u and controlling the growth of n via the estimates in the local theory

a new proof of global existence for the dirac klein gordon equations in one space dimension abstract using a method of s klainerman and m machedon we give a new proof of global existence for the coupled dirac and klein gordon equations in one space dimension

reliable decentralized supervisory control of fuzzy discrete event systems decentralized supervisory control has been introduced to deal with a class of fuzzy discrete event systems des in which state transitions are uncertain in this paper we develop the work on fuzzy des to consider the reliable decentralized supervisor problem with possible failures of some local supervisors by presenting a new definition of co observable language the reliable decentralized supervisory control problem is solved since the co observable languages are not closed under union a new normal language that is co observable is defined to solve the synthesis problem finally a numerical example is given

observer based fuzzy adaptive control for strict feedback nonlinear systems in this paper a new fuzzy adaptive control approach is developed for a class of siso strict feedback nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is introduced for state estimation as well as system identification under the framework of the backstepping design fuzzy adaptive output feedback control is constructed recursively it is proven that the proposed fuzzy adaptive control approach guarantees the semi global boundedness property for all the signals and the tracking error to a small neighborhood of the origin simulation studies are included to illustrate the effectiveness of the proposed approach

kinked cracks in an anisotropic plane modeled by an integral equation method a boundary integral method for cracks in an anisotropic material is presented the method is based on the integral equation for the resultant forces along the cracks the integral kernels contain only a weak logarithmic singularity which simplifies the numerical implementation crack closure is also taken into account in the numerical formulation numerical tests are presented to illustrate the efficiency and the reliability of the proposed method

numerical solution of integral equations 1 a survey of boundary integral equation methods for the numerical solution of laplace s equation in three dimensions 2 superconvergence 3 perturbed projection methods for various classes of operator and integral equations 4 numerical solution of parallel processors of two point boundary value problems of astrodynamics 5 introduction to the numerical solution of cauchy singular integral equations 6 convergence theorems for singular integral equations 7 planing surfaces 8 abel integral equations

sharp ill posedness of the dirac klein gordon system in one dimension abstract we show the ill posedness of the cauchy problem for the dirac klein gordon system in one dimension in the critical sobolev space from this we finish the classification of the regularities for which this problem is well posed or ill posed

analytic well posedness of periodic gkdv abstract in the periodic case it is proved that the cauchy problem for the generalized korteweg de vries equation gkdv is locally well posed in a class of analytic functions that can be extended holomorphically in a symmetric strip of the complex plane around the x axis thus the uniform analyticity radius of the solution does not change as time progresses also information about the regularity of the solution in the time variable is provided

numerical methods of singular integral equation for solving some problem in fluid dynamic consider a contact problem of two different layers under certain conditions the aim of this work is obtaining the stress potential function between the two layers and obtaining the solution numerically using two different method toeplitz matrix method and product nystrom method numerical results are considered and the error in each case is computed

finite energy solutions of the yang mills equations in mathbb r 3 1 yang mills equations in r3 1 is well posed in the energy norm this means that for an appropriate gauge condition we construct local unique solutions in a time interval which depends only on the size of the energy norm of the data since the energy norm is left invariant by the yang mills flow the local solution is automatically extended to the entire space time thus our results which settle a problem stated in str imply the well known fundamental regularity result of eardley and moncrief e m that result proved in the temporal gauge requires a higher degree of smoothness for the data our main result proved also in the temporal gauge allows us to extend the concept of solutions to arbitrary finite energy initial data the solutions are automatically unique in the class of solutions obtained by our procedure moreover the global regularity proof given by eardley and moncrief depends in an essential way on the specific properties of the fundamental solution of the wave equation in the flat minkowski space time r3 1 namely the strong huygens principle indeed due mainly to this fact their proof does not seem to extend to general curved space times we have reasons to hope that the very different approach we take here will resolve this difficulty the basic ingredients of our method are 1 the introduction of appropriate local coulomb gauges adapted to the causal structure of the equations 2 an appropriate method of localizing the new space time estimates for

on the radius of spatial analyticity for cubic nonlinear schrodinger equations abstract it is shown that the uniform radius of spatial analyticity t of solutions at time t to the 1d 2d and 3d cubic nonlinear schrodinger equations cannot decay faster than 1 t as t given initial data that is analytic with fixed radius 0

numerical solution of integral equations with a logarithmic kernel by the method of arbitrary collocation points an integral equation whose kernel presents logarithmic singularity is numerically solved by the method of arbitrary collocation points acp as a first step a gaussian quadrature of order n hence of polynomial accuracy 2n 1 is employed for the numerical approximation of the integral until now the collocation which follows was performed on special points xk determined as roots of appropriate transcedental functions in order to retain the 2n 1 degree of polynomial accuracy of the gaussian quadrature in this paper an appropriate interpolatory technique is proposed so that xk may be arbitrary and yet the high 2n 1 accuracy of the gaussian quadrature is retained

efficient methods for highly oscillatory integrals with weakly singular and hypersingular kernels abstract in this paper we present a special clenshaw curtis filon ccf type scheme for approximation of highly oscillatory integrals with weak and hypersingular kernels the non oscillatory and nonsingular part of the integrand is replaced by a special hermite interpolation polynomial error bounds with respect to the frequency k and the number of the clenshaw curtis points n are considered the overall computational complexity for the scheme is o nlog n numerical experiments support the theoretical analysis

fractal strichartz estimate for the wave equation abstract we consider strichartz estimates for the wave equation with respect to general measures which satisfy certain growth conditions in r 3 1 we obtain the sharp estimate and in higher dimensions improve the previous results

on the radius of spatial analyticity for the 1d dirac klein gordon equations abstract we study the well posedness of the dirac klein gordon system in one space dimension with initial data that have an analytic extension to a strip around the real axis it is proved that the radius of analyticity t of the solutions at time t cannot decay faster than 1 t 4 as t

two end variable singularity boundary elements and their applications in crack crack interaction problems summary two new boundary elements have been proposed for simulation of variable order singularities at the two ends of an element in two dimensions the rst can model the variable order strain singularity at both the ends of the element the second element can do both the strain and traction singularities simultaneously the elements are useful for studying the interaction of singularities as in the case of multiple neighbouring cracks in a domain they are employed here for the computation of stress intensity factors sifs in the crack crack interaction problems to improve the accuracy of such computations further a modi ed crack closure integral mcci based method for mechanical and or thermal loading is presented examples of mode i crack and mixed mode problems under mechanical loading are studied to illustrate the performance of the proposed elements and the mcci based calculations the e ects of the order of gauss quadrature associated with such elements on the accuracy of the sifs are also reported copyright 2000 john wiley sons ltd

quadrature rules for weakly singular strongly singular and hypersingular integrals in boundary integral equation methods we present n point gauss gegenbauer quadrature rules for weakly singular strongly singular and hypersingular integrals that arise in integral equation formulations of potential problems in domains with edges and corners the rules are tailored to weight functions with algebraic endpoint singularities related to the geometrical singularities of the domain each rule has two different expressions involving legendre functions and hypergeometric functions respectively numerical examples amply demonstrate the accuracy and stability of the proposed algorithms application to the solution of a singular integral equation is exemplified

contact problems of kinked cracks modelled by a boundary integral method based on the integral equation for the resultant forces along a crack a numerical method is developed for the solution of two dimensional kinked crack problems taking crack contact into account the method is demonstrated by a consideration of an elastic half plane containing a piece wise straight line crack two numerical examples are presented and compared to finite element calculations the numerical results indicate that the present method can be an effective and reliable tool for investigations of kinked crack problems associated with crack contact

h tracking adaptive fuzzy integral sliding mode control for parallel manipulators abstract highly nonlinear coupling phenomenon is an inherently inevitable in parallel manipulators in which limbs links undergo rotating and sliding with without fixed base in this paper an h tracking adaptive fuzzy integral sliding mode control scheme is proposed for controlling parallel manipulators with nonlinear unmodeled dynamics external disturbances and limb to limb couples in which each coupled uncertainty is assumed to be bounded by an unknown gain the dynamics of the parallel manipulator is formulated as an error dynamics according to a specified reference model then a fuzzy model is used to approximate the uncertainties two on line estimation schemes are developed to overcome the uncertainties and identify the gains of the unknown coupled uncertainty bounds from limb to limb couples simultaneously the advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear uncertain functions with an on line update law by the concept of parallel distributed compensation pdc the adaptive fuzzy scheme uses an integral sliding mode control scheme to resolve the system uncertainties unknown limb to limb coupled uncertainties and the external disturbances such that h tracking performance is achieved the control laws are derived based on a lyapunov criterion and the riccati inequality such that all states of the system are uniformly ultimately bounded uub and the effect on the tracking error can be attenuated to any prescribed level to achieve h tracking performance finally a numerical example of a planar 2 dof parallel robot system is given to verify the effectiveness of the proposed control scheme

fuzzy adaptive observer backstepping control for mimo nonlinear systems in this paper a fuzzy adaptive backstepping output feedback control approach is developed for a class of multi input and multi output mimo nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is designed for state estimation as well as system identification combining with the backstepping design techniques a fuzzy adaptive output feedback control is constructed recursively it is proved that the proposed fuzzy adaptive control approach can guarantee the semi global uniform ultimate boundedness for all the signals and the tracking error to a small neighborhood of the origin simulation studies illustrate the effectiveness of the proposed approach

a four node plate bending element based on mindlin reissner plate theory and a mixed interpolation this communication discusses a 4 node plate bending element for linear elastic analysis which is obtained as a special case from a general nonlinear continuum mechanics based 4 node shell element formulation the formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate and shell element

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

numerical solution of integral equations with logarithmic cauchy and hadamard type singularities this study presents an extension of the piecewise quadratic polynomial technique to solve singular integral equations with logarithmic and hadamard type singularities for completeness and continuity the evaluation of the weights for logarithmic cauchy and hadamard type singularities are given explicitly numerical results concerning logarithmic and hadamard type singular integral equations are compared with the known solutions the solution of cauchy type singular integral equations was discussed in detail in a previous study by miller and keer 1998 john wiley sons ltd

new lower bounds on the radius of spatial analyticity for the kdv equation abstract the radius of spatial analyticity for solutions of the kdv equation is studied it is shown that the analyticity radius does not decay faster than t 1 4 as time t goes to infinity this improves the works of selberg and da silva 2017 30 and tesfahun 2017 34 our strategy mainly relies on a higher order almost conservation law in gevrey spaces which is inspired by the i method

the cauchy problem of a periodic higher order kdv equation in analytic gevrey spaces abstract this paper studies the periodic cauchy problem for a kdv equation whose dispersion is of order m 2 j 1 where j is a positive integer kdvm using bourgain gevrey type analytic spaces and appropriate bilinear estimates it is shown that local in time well posedness holds when the initial data belong to an analytic gevrey spaces of order this implies that in the space variable the regularity of the solution remains the same with that of the initial data it also implies that the size of the uniform radius of analyticity is preserved moreover the solution is not necessarily g in time however it belongs to g m r near zero for every x on the circle

fuzzy adaptive controller for mimo nonlinear systems with known and unknown control direction this paper investigates fuzzy adaptive control schemes for a class of multi input multi output mimo unknown nonlinear systems with known and unknown sign of the control gain matrix three fuzzy adaptive control schemes are developed in the design of the second and third controller we will exploit a decomposition of the control gain matrix into a symmetric positive definite matrix a diagonal matrix with diagonal entries 1 or 1 and a unity upper triangular matrix the nussbaum type function is used to deal with the unknown control direction i e the unknown sign of the control gain matrix for updating the parameters of the fuzzy system an adaptation proportional integral pi law is proposed theoretical results are illustrated through two simulation examples

on the consideration of unilateral contact and friction in cracks the boundary integral method the scope of the present paper is the study of cracks having a given geometry by taking into account unilateral contact and friction phenomena between the two sides of the crack the arising problem is highly non classical because of the inequality relations describing the unilateral contact and friction interface conditions the indirect biem is extended appropriately in order to treat this problem numerical examples concerning the calculation of stress intensity factors under the unilateral contact and friction interface conditions illustrate the developed method

holomorphic extension of solutions of semilinear elliptic equations abstract we prove sharp analytic estimates and holomorphic extensions in sectors of c d for the solutions of a wide class of semilinear elliptic differential and pseudodifferential equations in r d improving earlier results where the extension was shown for a strip moreover we derive exponential decay estimates for such extended solutions the results presented apply in particular to solitary wave solutions of many classical nonlinear evolution equations as kdv type long wave type and schrodinger equations

global solutions and asymptotic behaviors of the chern simons dirac equations in r1 1 abstract the initial value problem of the chern simons dirac equations in one space dimension is studied we prove the existence of global solution and investigate asymptotic behaviors

unilateral contact friction and related interactions in cracks the direct boundary integral method abstract the paper presents a theory for the study of cracks having a given geometry by taking into account all types of actions of monotone type like unilateral contact and friction phenomena between the two crack sides the arising problems are of a non classical nature due to the interface conditions expressed in terms of non differentiable convex superpotentials the direct b i e m is extended appropriately in order to treat this type of problem the developed method is illustrated by a numerical example concerning the calculation of stress intensity factors under the unilateral contact and friction interface conditions

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

sharp local well posedness results for the nonlinear wave equation this article is concerned with local well posedness of the cauchy problem for second order quasilinear hyperbolic equations with rough initial data the new results obtained here are sharp in low dimension

global existence of small analytic solutions to nonlinear schrodinger equations in this paper we consider the following nonlinear schrodinger equation in r n n 2 i u 1 2 u f u u u t x er r n u 0 x x xer n

dynamic crack analysis in piezoelectric solids with non linear electrical and mechanical boundary conditions by a time domain bem abstract this paper presents advanced transient dynamic crack analysis in two dimensional 2d homogeneous and linear piezoelectric solids using non linear mechanical and electrical crack face boundary conditions stationary cracks in infinite and finite piezoelectric solids subjected to impact loadings are considered for this purpose a time domain boundary element method tdbem is developed a galerkin method is implemented for the spatial discretization while a collocation method is applied for the temporal discretization an explicit time stepping scheme is obtained to compute the unknown boundary data including the generalized crack opening displacements cods numerically an iterative solution algorithm is developed to consider the non linear semi permeable electrical crack face boundary conditions furthermore an additional iteration scheme for crack face contact analysis is implemented at time steps when a physically meaningless crack face intersection occurs several numerical examples are presented and discussed to show the effects of the electrical crack face boundary conditions on the dynamic intensity factors

piecewise integral sliding mode control for t s fuzzy systems this paper addresses the issue of piecewise integral sliding mode control ismc for the takagi sugeno t s fuzzy systems ismc is chosen to stabilize the t s fuzzy system because of its superior capability in treating uncertainties individual integral sliding surfaces are designed in different operating regions of the t s fuzzy system conditions on the existence of the sliding mode in the associated region are given the chattering phenomenon around region boundaries is analyzed and the prevention of such chattering is discussed an illustrative example is finally given to show the efficiency of the proposed method