distributed lagrange multipliers based on fictitious domain method for second order elliptic problems in this article we further investigate the solution of linear second order elliptic boundary value problems by distributed lagrange multipliers based fictitious domain methods the following issues are addressed i derivation of the fictitious domain formulations ii finite element approximation iii iterative solution of the resulting finite dimensional problems of the saddle point type by preconditioned conjugate gradient and lanczos algorithms

global existence and regularity of solutions to a system of nonlinear maxwell equations abstract we consider the model that has been suggested by greenberg et al physica d 134 1999 362 383 for the ferroelectric behavior of materials in this model the usual linear maxwell s equations are supplemented with a constitutive relation in which the electric displacement equals a constant times the electric field plus an internal polarization variable which evolves according to an internal set of nonlinear maxwell s equations for such model we provide rigorous proofs of global existence uniqueness and regularity of solutions we also provide some preliminary results on the long time behavior of solutions the main difficulties in this study are due to the loss of compactness in the system of maxwell s equations these results generalize those of greenberg et al where only solutions with tm transverse magnetic symmetry were considered

global weak solutions to a spatio temporal fractional landau lifshitz bloch equation abstract the present paper deals with global existence of weak solutions of a time space fractional landau lifshitz bloch equation involving the weak caputo derivative and a fractional laplacian we use faedo galerkin method with some commutator estimates in order to prove global existence of weak solutions for the model the uniqueness is also discussed in a special one dimensional case

schrodinger maps and anti ferromagnetic chains we study the problem of restricting schrodinger maps onto lagrangian submanifolds the restriction is imposed by an infinite constraining potential we show that in the limit solutions of the schrodinger map equations converge to solutions of generalized wave map equations this result is applied to the anti ferromagnetic systems where we prove rigorously that the dynamics is governed by wave map equations into open image in new window

local and nonlocal continuum modeling of inelastic periodic networks applied to stretching dominated trusses we present a nonlocal continuum model and its numerical implementation to describe the macroscale response of periodic discrete networks via second order homogenization the scale bridging technique is applied to the specific example of stretching dominated elastic and inelastic periodic truss networks experiments on small scale truss structures have highlighted the importance of nodal connections on the effective stiffness and strength therefore we describe the mechanics of trusses by accounting for the stretching of truss members and the deformation of nodes for the representative 2d examples of lattices having square and triangular architectures and for example bar and nodal constitutive laws we show that a simple continuum model based on affinely deforming a representative unit cell is sufficient to reproduce the nonlinear elastic behavior of discrete trusses by contrast localization that arises e g from inelastic deformation requires a refined model this is where the presented nonlocal continuum model is capable of accurately capturing details of localized deformation we illustrate the performance of the model by comparing the results of example finite element simulations using the continuum constitutive model to discrete lattice calculations with elastic plastic bars optimal performance is achieved when the representative unit cell of the continuum model agrees with the actual size of the discrete truss unit cell which accounts for size effects even in regimes where a separation of scales between finite element size and unit cell size does not strictly apply

random attractors for the stochastic coupled fractional ginzburg landau equation with additive noise this paper is concerned with the stochastic coupled fractional ginzburg landau equation with additive noise we first transform the stochastic coupled fractional ginzburg landau equation into random equations whose solutions generate a random dynamical system then we prove the existence of random attractor for random dynamical system

an unfitted hp adaptive finite element method based on hierarchical b splines for interface problems of complex geometry generating finite element discretizations with direct interface parameterizations constitutes a considerable computational expense in case of complex interface geometries the paper at hand introduces a b spline finite element method which circumvents parameterization of interfaces and offers fast and easy meshing irrespective of the geometric complexity involved its core idea is the adaptive approximation of discontinuities by hierarchical grid refinement which adds several levels of local basis functions in the close vicinity of interfaces but unfitted to their exact location so that a simple regular grid of knot span elements can be maintained numerical experiments show that an hp refinement strategy which simultaneously increases the polynomial degree of the b spline basis and the levels of refinement around interfaces achieves exponential rates of convergence despite the presence of discontinuities it is also demonstrated that the hierarchical b spline fem can be used to transfer the recently introduced finite cell concept to geometrically nonlinear problems its computational performance imposition of unfitted boundary conditions and fast hierarchical grid generation are illustrated for a set of benchmark problems in one two and three dimensions and the advantages of the regular grid approach for complex geometries are demonstrated by the geometrically nonlinear simulation of a voxel based foam composite

on the euler equations of incompressible fluids euler equations of incompressible fluids use and enrich many branches of mathematics from integrable systems to geometric analysis they present important open physical and mathematical problems examples include the stable statistical behavior of ill posed free surface problems such as the rayleightaylor and kelvin helmholtz instabilities the paper describes some of the open problems related to the incompressible euler equations with emphasis on the blowup problem the inviscid limit and anomalous dissipation some of the recent results on the quasigeostrophic model are also mentioned

the hp d adaptive finite cell method for geometrically nonlinear problems of solid mechanics summary the finite cell method fcm combines the fictitious domain approach with the p version of the finite element method and adaptive integration for problems of linear elasticity it offers high convergence rates and simple mesh generation irrespective of the geometric complexity involved this article presents the integration of the fcm into the framework of nonlinear finite element technology however the penalty parameter of the fictitious domain is restricted to a few orders of magnitude in order to maintain local uniqueness of the deformation map as a consequence of the weak penalization nonlinear strain measures provoke excessive stress oscillations in the cells cut by geometric boundaries leading to a low algebraic rate of convergence therefore the fcm approach is complemented by a local overlay of linear hierarchical basis functions in the sense of the hp d method which synergetically uses the h adaptivity of the integration scheme numerical experiments show that the hp d overlay effectively reduces oscillations and permits stronger penalization of the fictitious domain by stabilizing the deformation map the hp d adaptive fcm is thus able to restore high convergence rates for the geometrically nonlinear case while preserving the easy meshing property of the original fcm accuracy and performance of the present scheme are demonstrated by several benchmark problems in one two and three dimensions and the nonlinear simulation of a complex foam sample copyright 2011 john wiley sons ltd

asymptotic behavior of stochastic fractional power dissipative equations on rn abstract we study a reaction fractional diffusion equation with additive noise on the entire space r n with particular interest in the asymptotic behavior of solutions we first transform the equation into a random equation whose solutions generate a random dynamical system a priori estimates for solutions are derived when the nonlinearity satisfies certain growth conditions using estimates for far field values of solutions and a cut off technique asymptotic compactness is proved thus the existence of a random attractor in l 2 r n is established

multi valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems multi valued solutions are constructed for 2 2 first order systems using a generalization of the hodograph transformation the solution is found as a complex analytic function on a complex riemann surface for which the branch points move as part of the solution the branch point singularities are envelopes for the characteristics and thus move at the characteristic speeds we perform an analysis of stability of these singularities with respect to perturbations of the initial data the generic singularity types are folds cusps and nondegenerate umbilic points with non zero 3 jet an isolated singularity is generically a square root branch point corresponding to a fold two types of collisions between singularities are generic at a tangential collision between two singularities moving at the same characteristic speed a cube root branch point is formed corresponding to a cusp a non tangential collision between two square root branch points moving at different characteristic speeds remains a square root branch point at the collision and corresponds to a nondegenerate umbilic point these results are also valid for a diagonalizable n th order system for which there are exactly two speeds 1993 john wiley sons inc

finite element analysis on implicitly defined domains an accurate representation based on arbitrary parametric surfaces in this paper we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis the novel contributions of this paper are threefold 1 describe and validate a method to represent arbitrary parametric surfaces implicitly 2 represent arbitrary solids implicitly including sharp features using level sets and boolean operations 3 impose arbitrary dirichlet and neumann boundary conditions on the resulting implicitly defined boundaries the methods proposed do not require local refinement of the finite element mesh in regions of high curvature ensure the independence of the domain s volume on the mesh do not rely on boundary regularization and are well suited to methods based on fixed grids such as the extended finite element method xfem numerical examples are presented to demonstrate the robustness and effectiveness of the proposed approach and show that it is possible to achieve optimal convergence rates using a fully implicit representation of object boundaries this approach is one step in the desired direction of tying numerical simulations to computer aided design cad similarly to the isogeometric analysis paradigm

well posedness and dynamics of stochastic fractional model for nonlinear optical fiber materials abstract the current paper is devoted to the well posedness and dynamics of the stochastic coupled fractional ginzburg landau equation which describes a class of nonlinear optical fiber materials with active and passive coupled cores by the commutation estimates and fourier galerkin approximation the global existence of weak solutions and the uniqueness criterion are established moreover the existence of a global attractor is shown finally we consider the long time behavior of the stochastic coupled fractional ginzburg landau equation scfgl with multiplicative noise and prove the existence of a random attractor for the random dynamical system generated by the scfgl equation

dynamics of the 3 d fractional complex ginzburg landau equation abstract we study the initial boundary value problem of the fractional complex ginzburg landau equation in three spatial dimensions with the dissipative effect given by a fractional laplacian a priori estimates are derived when the nonlinearity satisfies certain growth conditions using galerkin s method the existence of a global smooth solution is established uniqueness is also proved furthermore the existence of a global attractor is proved and estimates of the hausdorff and fractal dimensions for the global attractor are obtained

maxwell s equations with vector hysteresis electromagnetic processes in magnetic materials are described by maxwell s equations in ferrimagnetic insulators assuming that d e e we have the equation

asymptotic behavior for non autonomous fractional stochastic ginzburg landau equations on unbounded domains in this paper we first prove the existence and uniqueness of tempered pullback random attractors for a non autonomous stochastic fractional ginzburg landau equation driven by multiplicative noise with 0 1 in l2r3 then we obtain the upper semicontinuity of random attractors when the intensity of noise approaches zero due to the lack of the compactness of sobolev embeddings on unbounded domains we establish the pullback asymptotic compactness of solutions in l2 r3 by the tail estimates of solutions

on the long time behavior of ferroelectric systems abstract this paper presents a new model for the ferroelectric behavior of materials the usual maxwell s equations are supplemented with a constitutive relation in which the electric displacement equals a constant times the electric field plus an internal polarization variable the latter evolves according to an internal set of maxwell equations this model is suggested by one presented by one of the authors for elastic behavior with phase change the model admits hysteretic behavior the asymptotic behavior with respect to time is studied and it is shown that the system tends to a steady state in which the polarization is governed by a nonlinear elliptic equation it is shown that this equation has multiple solutions which correspond to microstructure

the finite cell method for linear thermoelasticity the recently introduced finite cell method fcm combines the fictitious domain idea with the benefits of high order finite elements while previous publications concentrated on single field applications this paper demonstrates that the advantages of the method carry over to the multi physical context of linear thermoelasticity the ability of the method to converge with exponential rates is illustrated in detail with a benchmark problem a second example shows that the finite cell method correctly captures the thermoelastic state of a complex problem from engineering practice both examples additionally verify that also for two field problems dirichlet boundary conditions can be weakly imposed on non conforming meshes by the proposed extension of nitsche s method

an efficient integration technique for the voxel based finite cell method the finite cell method is a fictitious domain approach based on hierarchical ansatz spaces of higher order the method avoids time consuming and often error prone mesh generation and favorably exploits cartesian grids to embed structures of complex geometry in a simple shaped computational domain thus shifting parts of the computational effort from mesh generation to the computation within the embedding finite cells of regular shape this paper presents an effective integration approach for voxel based models of linear elasticity that drastically reduces the computational effort on cell level the applied strategy allows the pre computation of an essential part of the cell matrices and vectors of higher order representing stiffness and load respectively several benchmark problems show the potential of the proposed method in particular for heterogeneous material properties as common in biomedical applications based on computer tomography scans the applied strategy ensures a fast computation for time critical simulations and even allows user interactive simulations for models of moderate size at a high level of accuracy

smooth solution to the one dimensional inhomogeneous non automorphic landau lifshitz equation using the differential difference method and viscosity vanishing approach we obtain the existence and uniqueness of the global smooth solution to the periodic initial value problem of the inhomogeneous non automorphic landau lifshitz equation without gilbert damping terms in one dimension to establish the uniform estimates we use some identities resulting from the fact jz x t jz 1 and the fact that the vectors fz z x z z xg form an orthogonal base of the space r 3

global weak solution for the landau lifshitz maxwell equation in three space dimensions abstract in this paper by using an a priori estimate and the galerkin method the global existence of a weak solution for the landau lifshitz maxwell equations in three dimension is proved

existence and upper semicontinuity of random attractors for non autonomous fractional stochastic ginzburg landau equations this paper deals with the dynamical behavior of solutions for nonautonomous stochastic fractional ginzburg landau equations driven by multiplicative noise with 0 1 we first transform the stochastic equation into a random equation the solutions of which generate a random dynamical system consequently we establish the existence and uniqueness of tempered pullback random attractors for the equations in a bounded domain finally we obtain the upper semicontinuity of random attractors when the intensity of noise approaches zero

global weak solutions of the fractional landau lifshitz maxwell equation abstract the fractional landau lifshitz maxwell equation is considered in this paper we show the global existence of suitable weak solutions by galerkin method and the vanishing viscosity method the main difficulties in this study are due to the loss of compactness of this system and the fact that the nonlinear term is nonlocal and of the same order of the equation to overcome these difficulties we introduce the commutator estimates and some cancellation properties to this equation which prove to be proper tools in the study of landau lifshitz type equations

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

dynamical behavior of non autonomous fractional stochastic reaction diffusion equations abstract in this paper we investigate the asymptotic behavior of solutions for the non autonomous fractional stochastic reaction diffusion equations driven by multiplicative noise with s 0 1 we prove the existence and uniqueness of tempered pullback random attractors for the equations in a bounded domain u by the compactness of sobolev embedding h s u l 2 u which is different from the previous work 46