contact models leading to variational hemivariational inequalities abstract a frictional contact model under the small deformations hypothesis for static processes is considered we model the behavior of the material by a constitutive law using the subdifferential of a proper convex and lower semicontinuous function the contact is described with a boundary condition involving clarke s generalized gradient our study focuses on the weak solvability of the model based on a fixed point theorem for set valued mappings we prove the existence of at least one weak solution the uniqueness the boundedness and the stability of the weak solution are also discussed the investigation is based on arguments in the theory of variational hemivariational inequalities finally we present several examples of constitutive laws and friction laws for which our theoretical results are valid

the proper dissipative extensions of a dual pair let a and widetilde a be dissipative operators on a hilbert space mathcal h and let a widetilde a form a dual pair i e a subset widetilde a resp widetilde a subset a we present a method of determining the proper dissipative extensions widehat a of this dual pair i e a subset widehat a subset widetilde a provided that mathcal d a cap mathcal d widetilde a is dense in mathcal h applications to symmetric operators symmetric operators perturbed by a relatively bounded dissipative operator and more singular differential operators are discussed finally we investigate the stability of the numerical range of the different dissipative extensions

on abstract grad div systems abstract for a large class of dynamical problems from mathematical physics the skew selfadjointness of a spatial operator of the form a 0 c c 0 where c d c h 0 h 1 is a closed densely defined linear operator between hilbert spaces h 0 h 1 is a typical property guided by the standard example where c grad 1 n and c div subject to suitable boundary constraints an abstract class of operators c c 1 c n is introduced hence the title as a particular application we consider a non standard coupling mechanism and the incorporation of diffusive boundary conditions both modeled by setting associated with a skew selfadjoint spatial operator a

passivity based control of implicit port hamiltonian systems with holonomic constraints abstract implicit port hamiltonian representations of mechanical systems are considered from a control perspective energy shaping is used for the purpose of stabilizing a desired equilibrium when using implicit models the problem turns out to be a simple quadratic programming problem as opposed to the partial differential equations that need to be solved when using explicit representations the described approach is generalized to address the problem of stabilization of homoclinic orbits thus leading to the formulation of swing up strategies for underactuated systems

well posedness for a general class of differential inclusions abstract we consider an abstract class of differential inclusions which covers differential algebraic and non autonomous problems as well as problems with delay under weak assumptions on the operators involved we prove the well posedness of those differential inclusions in a pure hilbert space setting moreover we study the causality of the associated solution operator the theory is illustrated by an application to a semistatic quasilinear variant of maxwell s equations

on reduced convex qp formulations of monotone lcps techniques for transforming convex quadratic programs qps into monotone linear complementarity problems lcps and vice versa are well known we describe a class of lcps for which a reduced qp formulation one that has fewer constraints than the standard qp formulation is available we mention several instances of this class including the known case in which the coefficient matrix in the lcp is symmetric

detection of arbitrarily many solutions for perturbed elliptic problems involving oscillatory terms we propose a direct approach for detecting arbitrarily many solutions for perturbed elliptic problems involving oscillatory terms although the method works in various frameworks we illustrate it on the problem

variational identities and applications to differential systems j serrin 1 introduction in the work of ponos p and in recent work of pucci serrin ps variational identities are discussed which are useful for solving various ques tions about elliptic differential equations and particular elliptic systems here we obtain a number of further applications of these identities to systems it was noted in ps that these identities are closely related to noether s theorem for variational problems by working out the divergence term arising in noether s theorem and making some simplifications one obtains a general identity for variational problems if a variational integral has a symmetry group g with the following infinitesimal generator

stabilization of a class of underactuated mechanical systems via interconnection and damping assignment we consider the application of a formulation of passivity based control pbc known as interconnection and damping assignment ida to the problem of stabilization of underactuated mechanical systems which requires the modification of both the potential and the kinetic energies our main contribution is the characterization of a class of systems for which ida pbc yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction the class is given in terms of solvability of certain partial differential equations one important feature of ida pbc stemming from its hamiltonian formulation is that it provides new degrees of freedom for the solution of these equations using this additional freedom we are able to show that the method of controlled lagrangians in its original formulation may be viewed as a special case of our approach as illustrations we design asymptotically stabilizing ida pbcs for the classical ball and beam system and a novel inertia wheel pendulum

general over relaxed proximal point algorithm involving a maximal relaxed monotone mappings with applications abstract a general framework for the over relaxed proximal point algorithm based on the notion of a maximal relaxed monotonicity is developed and then the convergence analysis in the context of solving a general class of nonlinear implicit inclusion problems is explored furthermore some auxiliary results of interest involving a maximal relaxed monotone mappings in a hilbert space setting are included

dualization of generalized equations of maximal monotone type this paper develops a simple duality framework for generalized equations defined by set valued mappings from a linear space to another the original problem is related to two auxiliary problems of the similar form corresponding to lagrangian and dual problems in the theory of convex programming as in convex programming the alternative formulations can be used to obtain information about a given problem and then used to solve it numerically in particular dualization can be used in deriving existence criteria for a given problem indirectly by considering one of the alternative formulations also a given problem can often be solved more easily by way of a dual method the strongest results of this paper concern monotone mappings in this context the duality framework yields several new criteria for maximal monotonicity of composite mappings these results are useful theoretically as well as in numerical solution of generalized equations the duality framework can also be used in problem decomposition since dualization can lead to reformulations to which operator splitting methods and other special methods can be applied

boundary optimal control for nonlinear antiplane problems abstract we consider a nonlinear antiplane problem which models the deformation of an elastic cylindrical body in frictional contact with a rigid foundation the contact is modelled with tresca s law of dry friction in which the friction bound is slip dependent the aim of this article is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target by acting with a control on the boundary of the body the existence of at least one optimal control is proved next we introduce a regularized problem depending on a small parameter and we study the convergence of the optimal controls when tends to zero an optimality condition is delivered for the regularized problem

composition duality and maximal monotonicity this paper shows how the attouch thera duality principle for operator inclusions can be extended to compositions of multifunctions so that the primal and dual inclusions may involve operators between different pairs of spaces we first present the extension and give an example from computational economics to demonstrate that it has practical utility then we consider a particular case often found in applications involving real hilbert spaces and maximal monotone operators we show that in this case our duality framework includes those previously developed by rockafellar mosco and gabay finally we demonstrate that in this case under very simple hypotheses the duality transformation preserves the maximal monotonicity of the operators involved this proof uses an apparently new criterion for maximal monotonicity of operators of the form l tl where t is maximal monotone and l is linear and continuous with adjoint l

dirac structures and boundary control systems associated with skew symmetric differential operators associated with a skew symmetric linear operator on the spatial domain a b we define a dirac structure which includes the port variables on the boundary of this spatial domain this dirac structure is a subspace of a hilbert space naturally associated with this dirac structure is an infinite dimensional system we parameterize the boundary port variables for which the c 0 semigroup associated with this system is contractive or unitary furthermore this parameterization is used to split the boundary port variables into inputs and outputs similarly we define a linear port controlled hamiltonian system associated with the previously defined dirac structure and a symmetric positive operator defining the energy of the system we illustrate this theory on the example of the timoshenko beam

solvability of dynamic antiplane frictional contact problems for viscoelastic cylinders abstract we study a mathematical model which describes the antiplane shear deformations of a cylinder in frictional contact with a rigid foundation the process is dynamic the material behavior is described with a linearly viscoelastic constitutive law and friction is modeled with a general subdifferential boundary condition we derive a variational formulation of the model which is in a form of an evolutionary hemivariational inequality for the displacement field then we prove the existence of a weak solution to the model the proof is based on an abstract result for second order evolutionary inclusions in banach spaces also we prove that under additional assumptions the weak solution to the model is unique we complete our results with concrete examples of friction laws for which our results are valid

hemivariational inequality for viscoelastic contact problem with slip dependent friction abstract in this paper we consider a class of hyperbolic hemivariational inequalities modeling the frictional contact between a viscoelastic body and a rigid foundation the friction law is described by a multivalued subdifferential relation which includes the slip displacement dependent friction and the tresca models we establish the existence of weak solutions to the problem by using a surjectivity result for pseudomonotone mappings

resolvent estimates in homogenisation of periodic problems of fractional elasticity we provide operator norm convergence estimates for solutions to a time dependent equation of fractional elasticity in one spatial dimension with rapidly oscillating coefficients that represent the material properties of a viscoelastic composite medium assuming periodicity in the coefficients we prove operator norm convergence estimates for an operator fibre decomposition obtained by applying to the original fractional elasticity problem the fourier laplace transform in time and gelfand transform in space we obtain estimates on each fibre that are uniform in the quasimomentum of the decomposition and in the period of oscillations of the coefficients as well as quadratic with respect to the spectral variable on the basis of these uniform estimates we derive operator norm type convergence estimates for the original fractional elasticity problem for a class of sufficiently smooth densities of applied forces

analysis of a dynamic contact problem for electro viscoelastic cylinders abstract we consider a mathematical model which describes the antiplane shear deformations of a piezoelectric cylinder in frictional contact with a foundation the process is mechanically dynamic and electrically static the material behavior is described with a linearly electro viscoelastic constitutive law the contact is frictional and the foundation is assumed to be electrically conductive both the friction and the electrical conductivity condition on the contact surface are described with subdifferential boundary conditions we derive a variational formulation of the problem which is of the form of a system coupling a second order hemivariational inequality for the displacement field with a time dependent hemivariational inequality for the electric potential field then we prove the existence of a unique weak solution to the model the proof is based on abstract results for second order evolutionary inclusions in banach spaces finally we present concrete examples of friction laws and electrical conductivity conditions for which our result is valid

passivity based control of implicit port hamiltonian systems the main contribution of this paper is the generalization of well known energy based control techniques i e energy balancing passivity based control passivity based control with state modulated source and interconnection and damping assignment passivity based control to the case in which the plant is a port hamiltonian system in implicit form a typical situation is when part of the system is obtained from the spatial discretization of an infinite dimensional port hamiltonian system in this case the dynamics is not given in standard input state output form but as a set of daes consequently the most popular control by energy shaping techniques have to be extended to deal with dynamical systems with constraints and geometrical conditions for the existence of the regulator based on the properties of dirac and resistive structures of the plant are also necessary the methodological results are discussed with the help of simple but illustrative examples in which the port hamiltonian systems in imp

on a new class of elliptic systems with nonlinearities of arbitrary growth abstract we guarantee the existence of infinitely many different pairs of solutions to the system u v p in v f u in u v 0 on where 0 p 2 n 2 is a bounded domain in r n and the continuous nonlinear term f has an unusual oscillatory behavior the sequence of solutions tends to zero resp infinity with respect to certain norms and the nonlinear term f may enjoy an arbitrary growth at infinity resp at zero whenever f oscillates near zero resp at infinity our results provide the first applications of ricceri s variational principle in the theory of coupled elliptic systems

general implicit variational inclusion problems based on a maximal m relaxed monotonicity amrm frameworks a general framework for an algorithmic procedure based on the variational convergence of operator sequences involving a maximal m relaxed monotone amrm mappings in a hilbert space setting is developed and then it is applied to approximating the solution of a general class of nonlinear implicit inclusion problems involving a maximal m relaxed monotone mappings furthermore some specializations of interest on existence theorems and corresponding approximation solvability theorems on h maximal monotone mappings are included that may include several other results for general variational inclusion problems on general maximal monotonicity in the literature

on lossless approximations the fluctuation dissipation theorem and limitations of measurements in this paper we take a control theoretic approach to answering some standard questions in statistical mechanics and use the results to derive limitations of classical measurements a central problem is the relation between systems which appear macroscopically dissipative but are microscopically lossless we show that a linear system is dissipative if and only if it can be approximated by a linear lossless system over arbitrarily long time intervals hence lossless systems are in this sense dense in dissipative systems a linear active system can be approximated by a nonlinear lossless system that is charged with initial energy as a by product we obtain mechanisms explaining the onsager relations from time reversible lossless approximations and the fluctuation dissipation theorem from uncertainty in the initial state of the lossless system the results are applied to measurement devices and are used to quantify limits on the so called observer effect also called back action which is the impact the measurement device has on the observed system in particular it is shown that deterministic back action can be compensated by using active elements whereas stochastic back action is unavoidable and depends on the temperature of the measurement device

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

on a first order hyperbolic system including bean s model for superconductors with displacement current abstract this paper deals with a class of first order systems with generally multivalued damping terms including bean s model for superconductors with displacement current the main goal is to prove the convergence of solutions to stationary states as t

multiple solutions for elliptic systems with nonlinearities of arbitrary growth abstract we prove the existence of infinitely many solutions for symmetric elliptic systems with nonlinearities of arbitrary growth moreover if the symmetry of the problem is broken by a small enough perturbation term we find at least three solutions the proofs utilise a variational setting given by de figueiredo and ruf in order to prove an existence s result and the algebraic approach based on the pohozaev s fibering method

on superquadratic elliptic systems in this article we study the existence of solutions for the elliptic system updelta u frac partial h partial v left u v x right text in upomega updelta v frac partial h partial v left u v x right text in upomega u 0 v 0 text on partial upomega where upomega is a bounded open subset of mathbb r n with smooth boundary partial upomega and the function h mathbb r 2 times overline upomega to mathbb r is of class c 1

mother operators and their descendants abstract a mechanism deriving new well posed evolutionary equations from given ones is inspected it turns out that there is one particular spatial operator from which many of the standard evolutionary problems of mathematical physics can be generated by this abstract mechanism using suitable projections the complexity of the dynamics of the phenomena considered can be described in terms of suitable material laws the idea is illustrated with a number of concrete examples

quaternionic time harmonic maxwell operator the theory of quaternionic alpha hyperholomorphic functions synonyms monogenic regular spatial holomorphic vectors is currently developing rapidly in particular many integral formulae with explicit reproducing kernels have been obtained in this work we establish a one to one correspondence between time harmonic monochromatic electromagnetic fields and pairs of mutually conjugate hyperholomorphic functions this leads to the cauchy type integral associated with maxwell s equations some main integral formulae for maxwell s equations involving this cauchy type integral are obtained it should be mentioned that in fact we introduce and study a somewhat more general quaternionic object which has better algebraic and analytic properties than the physical maxwell operator and which contains the latter as a special case

an alternative approach to well posedness of a class of differential inclusions in hilbert spaces we show the well posedness of initial value problems for differential inclusions of a certain type using abstract perturbation results for maximal monotone operators in hilbert spaces for this purpose the time derivative is established in an exponentially weighted l2 space the problem of well posedness then reduces to show that the sum of two maximal monotone operators in time and space is again maximal monotone the theory is exemplified by three inclusions describing phenomena in mathematical physics involving hysteresis

evolution hemivariational inequality for a class of dynamic viscoelastic nonmonotone frictional contact problems in this paper we consider a class of hyperbolic hemivariational inequalities modeling the frictional contact between a viscoelastic body and a rigid foundation the friction condition is described by a multivalued subdifferential relation which includes both the slip displacement and the slip rate dependent friction and the tresca models the existence of weak solutions to the problem is proved by exploiting a surjectivity result for a class of pseudomonotone mappings

implicit and explicit representations of continuous time port hamiltonian systems implicit and explicit representations of smooth nite dimensional port hamiltonian systems are studied from the perspective of their use in numerical simulation and control design implicit representations arise when a system is modeled in cartesian coordinates and when the system constraints are applied in the form of additional algebraic equations explicit representations are derived when generalized coordinates are used a relationship between the phase spaces for both system representations is derived in this article justifying the equivalence of the representations in the sense of preserving their hamiltonian functions as well as their hamiltonian symplectic forms ultimately resulting in the same hamiltonian ow

anti plane shear deformations in linear and nonlinear solid mechanics the intent of this expository paper is to draw the attention of the applied mathematics community to an interesting two dimensional mathematical model arising in solid mechanics involving a single second order linear or quasi linear partial differential equation this model has the virtue of relative mathematical simplicity without loss of essential physical relevance anti plane shear deformations are one of the simplest classes of deformations that solids can undergo in anti plane shear or longitudinal shear generalized shear of a cylindrical body the displacement is parallel to the generators of the cylinder and is independent of the axial coordinate thus anti plane shear with just a single scalar axial displacement field may be viewed as complementary to the more complicated yet perhaps more familiar plane strain deformation with its two in plane displacements in recent years considerable attention has been paid to the analysis of anti plane shear deformations within the context of variou

on a structural observation in generalized electromagnetic theory are satisfied equations 0 2 describe the electromagnetic properties of the medium where 0 1 is considered if this medium is confined to a certain region g of r3 then the electromagnetic properties of its complent cc are usually represented via boundary conditions on dg we shall deal here with the boundary condition appearing if cc is assumed to be a perfect conductor i e nxe t o on c7g 13 0 0 3

perturbation from dirichlet problem involving oscillating nonlinearities in this paper we prove that if the potential f x t 0tf x s ds has a suitable oscillating behavior in any neighborhood of the origin respectively then under very mild conditions on the perturbation term g for every k n there exists bk 0 such that u f x u g x u in u 0on has at least k distinct weak solutions in w01 2 for every r with bk moreover information about the location of such solutions is also given in fact there exists a positive real number 0 which does not depend on such that the w01 2 norm of each of those k solutions is not greater than

a characterization of boundary conditions yielding maximal monotone operators abstract we provide a characterization for maximal monotone realizations for a certain class of nonlinear operators in terms of their corresponding boundary data spaces the operators under consideration naturally arise in the study of evolutionary problems in mathematical physics we apply our abstract characterization result to port hamiltonian systems and a class of frictional boundary conditions in the theory of contact problems in visco elasticity

boundary relations and their weyl families the concepts of boundary relations and the corresponding weyl families are introduced let s be a closed symmetric linear operator or more generally a closed symmetric relation in a hilbert space h let h be an auxiliary hilbert space let graphics and let jh be defined analogously a unitary relation g from the krein space h 2 j h to the kre in space h 2 j h is called a boundary relation for the adjoint s if ker gamma s the corresponding weyl family m lambda is de ned as the family of images of the defect subspaces n over cap lambda lambda is an element of c r under gamma here gamma need not be surjective and is even allowed to be multi valued while this leads to fruitful connections between certain classes of holomorphic families of linear relations on the complex hilbert space h and the class of unitary relations gamma h 2 j h h 2 j h it also generalizes the notion of so called boundary value space and essentially extends the applicability of abstract boundary mappings in the connection of boundary value problems moreover these new notions yield for instance the following realization theorem every h valued maximal dissipative for lambda is an element of c holomorphic family of linear relations is the weyl family of a boundary relation which is unique up to unitary equivalence if certain minimality conditions are satisfied further connections between analytic and spectral theoretical properties of weyl families and geometric properties of boundary relations are investigated and some applications are given

a general variational principle and some of its applications abstract in this paper given a reflexive real banach space x and two sequentially weakly lower semicontinuous functionals on x with strongly continuous and coercive we are mainly interested in the existence of infinitely many local minima of the functional for each sufficiently large r

a mixed hemivariational variational problem and applications abstract we consider an abstract system with lagrange multipliers which consists of a hemivariational inequality and a variational inequality the hemivariational inequality is governed by a hemicontinuous generalized monotone possibly nonlinear operator as well as by a bilinear form this bilinear form also governs the variational inequality we are looking for a pair solution in a subset of a product of two real reflexive banach spaces in order to illustrate the applicability of the abstract results two examples in terms of pdes are delivered each example is related to the weak solvability of a boundary value problem arising in contact mechanics

on the range of the douglas rachford operator the problem of finding a minimizer of the sum of two convex functions or more generally that of finding a zero of the sum of two maximally monotone operators is of central importance in variational analysis perhaps the most popular method of solving this problem is the douglas rachford splitting method surprisingly little is known about the range of the douglas rachford operator in this paper we set out to study this range systematically we prove that for 3 monotone operators a very pleasing formula can be found that reveals the range to be nearly equal to a simple set involving the domains and ranges of the underlying operators a similar formula holds for the range of the corresponding displacement mapping we discuss applications to subdifferential operators to the infimal displacement vector and to firmly nonexpansive mappings various examples and counterexamples are presented including some concerning the celebrated brezis haraux theorem

weak solutions for nonlinear antiplane problems leading to hemivariational inequalities abstract we analyze the antiplane shear deformation of an elastic cylinder in frictional contact with a rigid foundation for static processes under the small deformation hypothesis based on the knaster kuratowski mazurkiewicz technique in the theory of the hemivariational inequalities we prove that the model has at least one weak solution moreover we present several examples of constitutive laws and friction laws for which our theoretical results are valid finally we comment on the conditions which guarantee the uniqueness of the solution

the relevance of convex analysis for the study of monotonicity abstract we introduce new representations for maximal monotone operators we relate them to previous representations given by krauss fitzpatrick martinez legaz and thera we show their usefulness for the study of compositions and sums of maximal monotone operators

strongly indefinite systems with critical sobolev exponents we consider an elliptic system of hamiltonian type on a bounded domain in the superlinear case with critical growth rates we obtain existence and positivity results for solutions under suitable conditions on the linear terms our proof is based on an adaptation of the dual variational method as applied before to the scalar case introduction existence and non existence of solutions of semilinear elliptic srstems has been a subject of active research recently see for example ff l3 ps such systems are called variational if solutions can be viewed as critical points of an associated functional defined on a suitable function space restricting our attention to systems with two unknowns we distinguish two classes of variational elliptic systems a potential systems b hamiltonian systems potential systems are of the form a llu u v ztl2v u v where l1 and l2 are second order selfadjoint elliptic operators formally these are the euler lagrange equations of the functional f u v l1u u i l2v v th u v here is the l2 inner product for functions defined on the underlying domain and tt u v s h u x v x dx the functional f is often called the lagrangian its critical points correspond to weak soltbtions of a the appropr ate choice of the function spaces for u and v follows by requiring that the quadratic part of f be well defined this naturally leads to sobolev spaces with square irltegrable first derivatives since also a must be well defined by virtue of the embedding theorems some growth restrictions on this latter function are required an extra difficulty appears if we consider system a with a plus sign in the second equation for then the corresponding functiorl f has a strongly indefinite quadratic part for systems of superlinear type and with sllbcritical growth the mountain pass theorem ar or in the strongly indefinite case the benci rabinowitz theorem received by the editors june 5 1996 1991 mathematics subject classification primary 35j50 35j55 35j65

interconnection of port hamiltonian systems and composition of dirac structures port based network modeling of physical systems leads to a model class of nonlinear systems known as port hamiltonian systems port hamiltonian systems are defined with respect to a geometric structure on the state space called a dirac structure interconnection of port hamiltonian systems results in another port hamiltonian system with dirac structure defined by the composition of the dirac structures of the subsystems in this paper the composition of dirac structures is being studied both in power variables and in wave variables scattering representation this latter case is shown to correspond to the redheffer star product of unitary mappings an equational representation of the composed dirac structure is derived furthermore the regularity of the composition is being studied necessary and sufficient conditions are given for the achievability of a dirac structure arising from the standard feedback interconnection of a plant port hamiltonian system and a controller port hamiltonian system and an explicit description of the class of achievable casimir functions is derived

generalized eckstein bertsekas proximal point algorithm based on a maximal monotonicity design a general design for the eckstein bertsekas proximal point algorithm using the notion of the a maximal monotonicity is developed convergence analysis for the generalized eckstein bertsekas proximal point algorithm in the context of solving a class of nonlinear inclusion problems is explored some auxiliary results of interest involving a maximal monotone mappings are also included the obtained results generalize investigations on general maximal monotonicity and beyond

dissipative extensions and port hamiltonian operators on networks abstract in this article we study port hamiltonian partial differential equations on certain one dimensional manifolds we classify those boundary conditions that give rise to contraction semigroups as an application we study port hamiltonian operators on networks whose edges can have finite or infinite length in particular we discuss possibly infinite networks in which the edge lengths can accumulate zero and port hamiltonian operators with hamiltonians that neither are bounded nor bounded away from zero we achieve this by first providing a new description for maximal dissipative extensions of skew symmetric operators the main technical tool used for this is the notion of boundary systems the latter generalizes the classical notion of boundary triple t s and allows to treat skew symmetric operators with unequal deficiency indices in order to deal with fairly general variable coefficients we develop a theory of possibly unbounded non negative injective weights on an abstract hilbert space

well posedness of non autonomous evolutionary inclusions a class of non autonomous differential inclusions in a hilbert space setting is considered the well posedness for this class is shown by establishing the mappings involved as maximal monotone relations moreover the causality of the so established solution operator is addressed the results are exemplified by the equations of thermoplasticity with time dependent coefficients and by a non autonomous version of the equations of viscoplasticity with internal variables

existence and uniqueness results for a class of quasi hemivariational inequalities abstract in this paper we are concerned with the study of a nonstandard quasi hemivariational inequality using a fixed point theorem for set valued mappings the existence of at least one solution in bounded closed and convex subsets is established we also provide sufficient conditions for which our inequality possesses solutions in the case of unbounded sets finally the uniqueness and the stability of the solution are analyzed in a particular case

the over relaxed proximal point algorithm based on h maximal monotonicity design and applications first the general framework for a generalized over relaxed proximal point algorithm using the notion of h maximal monotonicity also referred to as h monotonicity is developed and then the convergence analysis for this algorithm in the context of solving a general class of nonlinear inclusion problems is examined along with some auxiliary results on the resolvent operators corresponding to h maximal monotonicity

a dynamic viscoelastic contact problem with normal compliance a dynamic contact problem between a viscoelastic body and a deformable obstacle is numerically considered in this work the contact is modeled by using the well known normal compliance contact condition the variational formulation of this problem is written in terms of the velocity field and it leads to a parabolic nonlinear variational equation an existence and uniqueness result is stated fully discrete approximations are then introduced by using the finite element method to approximate the spatial variable and a hybrid combination of the implicit and explicit euler schemes to discretize the time derivatives an a priori error analysis is recalled then an a posteriori error analysis is provided extending some results already obtained in the study of the heat equation other parabolic equations and the quasistatic case upper and lower bounds are proved finally some two dimensional numerical simulations are presented to demonstrate the accuracy and the behavior of the error estimators