counter example in three dimension and homogenization of geometric motions in two dimension in this paper we give a counter example to the homogenization of the forced mean curvature motion in a periodic setting in dimension n geqq 3 when the forcing is positive we also prove a general homogenization result for geometric motions in dimension n 2 under the assumption that there exists a constant 0 such that every straight line moving with a normal velocity equal to is a subsolution for the motion we also present a generalization in dimension 2 where we allow sign changing normal velocity and still construct bounded correctors when there exists a subsolution with compact support expanding in all directions

a theory of independent fuzzy probability for system reliability fuzzy fault trees provide a powerful and computationally efficient technique for developing fuzzy probabilities based on independent inputs the probability of any event that can be described in terms of a sequence of independent unions intersections and complements may be calculated by a fuzzy fault tree unfortunately fuzzy fault trees do not provide a complete theory many events of substantial practical interest cannot be described only by independent operations thus the standard fuzzy extension based on fuzzy fault trees is not complete since not all events are assigned a fuzzy probability other complete extensions have been proposed but these extensions are not consistent with the calculations from fuzzy fault trees we propose a new extension of crisp probability theory our model is based on n independent inputs each with a fuzzy probability the elements of our sample space describe exactly which of the n input events did and did not occur our extension is complete since a fuzzy probability is assigned to every subset of the sample space our extension is also consistent with all calculations that can be arranged as a fault tree our approach allows the reliability analyst to develop complete and consistent fuzzy reliability models from existing crisp reliability models this allows a comprehensive analysis of the system computational algorithms are provided both to extend existing models and develop new models the technique is demonstrated on a reliability model of a three stage industrial process

weierstrass formula and zero finding methods classical weierstrass formula 29 has been often the subject of investigation of many authors in this paper we give some further applications of this formula for finding the zeros of polynomials and analytic functions we are concerned with the problems of localization of polynomial zeros and the construction of iterative methods for the simultaneous approximation and inclusion of these zeros conditions for the safe convergence of weierstrass method depending only on initial approximations are given in particular we study polynomials with interval coefficients using an interval version of weierstrass method enclosures in the form of disks for the complex valued set containing all zeros of a polynomial with varying coefficients are obtained we also present weierstrass like algorithm for approximating simultaneously all zeros of a class of analytic functions in a given closed region to demonstrate the proposed algorithms three numerical examples are included

on approximate zeros and rootfinding algorithms for a complex polynomial on donne des criteres pour qu un nombre complexe soit une racine approchee d un polynome f par la methode de newton ou d euler d ordre k on construit des familles d algorithmes surement convergents

periodic homogenisation of hamilton jacobi equations 2 eikonal equations homogenisation of the first order hamilton jacobi equations when h is periodic in the second variable leads to an effective hamiltonian h satisfying u e converges as e 0 to the solution u of u t h du 0 in our first paper we assumed that h is convex and we derived a variational formula giving h in this second paper we consider eikonal equations i e h p x p 2 v x using our variational formula we compute explicitly the effective hamiltonian in several cases and we study precisely the lack of strict convexity for h flat part around the origin

on the determination of the safe initial approximation for the durand kerner algorithm abstract in this paper applying the majorant function method we present a new proof of the convergence of the durand kerner method and obtain a greater computable radius estimation of safe initial discs this result is an improvement of all results now available furthermore combining the kuhn algorithm for solving all zeros of polynomials we obtain a discriminant to get safe initial discs finally we compare the complexity between the durand kerner algorithm and several known results and the numerical results show the superiority of our result

homogenization of weakly coupled systems of hamilton jacobi equations with fast switching rates we consider homogenization for weakly coupled systems of hamilton jacobi equations with fast switching rates the fast switching rate terms force the solutions to converge to the same limit which is a solution of the effective equation we discover the appearance of the initial layers which appear naturally when we consider the systems with different initial data and analyze them rigorously in particular we obtain matched asymptotic solutions of the systems and the rate of convergence we also investigate properties of the effective hamiltonian of weakly coupled systems and show some examples which do not appear in the context of single equations

nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints hamiltoniens sousquadratiques conditions aux limites infinies et donnees d explosion hamiltoniens superquadratiques formulation viscosite des conditions aux limites le probleme ergodique commande stochastique optimale avec contraintes d etat

on the large time behavior of solutions of hamilton jacobi equations associated with nonlinear boundary conditions in this article we study the large time behavior of solutions of first order hamilton jacobi equations set in a bounded domain with nonlinear neumann boundary conditions including the case of dynamical boundary conditions we establish general convergence results for viscosity solutions of these cauchy neumann problems by using two fairly different methods the first one relies only on partial differential equations methods which provides results even when the hamiltonians are not convex and the second one is an optimal control dynamical system approach named the weak kam approach which requires the convexity of hamiltonians and gives formulas for asymptotic solutions based on aubry mather sets

perron s method for hamilton jacobi equations on considere l existence des solutions d equations aux derivees partielles non lineaires scalaires d ordre 1 f x u du 0 dans ou est un sous ensemble ouvert de r n f r r n r est continue u r est l inconnue

fuzzy importance in fault tree analysis abstract in fault tree analysis system success or failure can be described by the state of the top event which is usually defined by a so called structure function in this paper we attempt to simplify the calculation process of the structure function and to newly define the state of the top event by the membership function using fuzzy sets theory furthermore it is shown that the importance of each basic event can be evaluated through fuzzy operations the method proposed herein is demonstrated by some examples with respect to the failure analysis of structures

a representation formula of viscosity solutions to weakly coupled systems of hamilton jacobi equations with applications to regularizing effect abstract based on a fixed point argument we give a dynamical representation of the viscosity solution to cauchy problem of certain weakly coupled systems of hamilton jacobi equations with continuous initial datum using this formula we obtain some regularity results related to the viscosity solution including a partial extension of lions regularizing effect 17 to the case of weakly coupled systems

point estimation of simultaneous methods for solving polynomial equations a survey ii the construction of computationally verifiable initial conditions which provide both the guaranteed and fast convergence of the numerical root finding algorithm is one of the most important problems in solving nonlinear equations smale s point estimation theory from 1981 was a great advance in this topic it treats convergence conditions and the domain of convergence in solving an equation f z 0 using only the information of f at the initial point z 0 the study of a general problem of the construction of initial conditions of practical interest providing guaranteed convergence is very difficult even in the case of algebraic polynomials in the light of smale s point estimation theory an efficient approach based on some results concerning localization of polynomial zeros and convergent sequences is applied in this paper to iterative methods for the simultaneous determination of simple zeros of polynomials we state new improved initial conditions which provide the guaranteed convergence of frequently used simultaneous methods for solving algebraic equations ehrlich aberth s method ehrlich aberth s method with newton s correction borsch supan s method with weierstrass correction and halley like or wang zheng method the introduced concept offers not only a clear insight into the convergence analysis of sequences generated by the considered methods but also explicitly gives their order of convergence the stated initial conditions are of significant practical importance since they are computationally verifiable they depend only on the coefficients of a given polynomial its degree n and initial approximations to polynomial zeros

continuum theory of epitaxial crystal growth i we present various continuum limits to describe epitaxial thin film growth we consider a hierarchy of models which can take into account the diffusion of terrace adatoms attachment and detachment of edge adatoms vapor phase diffusion and the effect of multiple species the starting point is the burton cabrera frank type step flow model we have obtained partial differential equations in the form of a coupled system of diffusion equation for the adatom density and a hamilton jacobi equation for the film height function this is supplemented with appropriate boundary conditions at the continuum level to describe the growth at the peaks and valleys on the film the results here can be used in a macroscopic description of thin film growth

higher order convergence rates in theory of homogenization iii viscous hamilton jacobi equations abstract in this paper we establish the higher order convergence rates in periodic homogenization of viscous hamilton jacobi equations which is convex and grows quadratically in the gradient variable we observe that although the nonlinear structure governs the first order approximation the nonlinear effect is absorbed as an external source term of a linear equation in the second and higher order approximation moreover we find that the geometric shape of the initial data has to be chosen carefully according to the effective hamiltonian in order to achieve the higher order convergence rates

fuzzy reliability assessment of systems with multiple dependent competing degradation processes components are often subject to multiple competing degradation processes for multicomponent systems the degradation dependence within one component or and among components need to be considered physics based models and multistate models are often used for component degradation processes particularly when statistical data are limited in this paper we treat dependence between degradation processes within a piecewise deterministic markov process pdmp modeling framework epistemic subjective uncertainty can arise due to the incomplete or imprecise knowledge about the degradation processes and the governing parameters to take this into account we describe the parameters of the pdmp model as fuzzy numbers then we extend the finite volume method to quantify the fuzzy reliability of the system the proposed method is tested on one subsystem of the residual heat removal system of a nuclear power plant and a comparison is offered with a monte carlo simulation solution the results show that our method can be most efficient

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

singular perturbations of nonlinear degenerate parabolic pdes a general convergence result the main result of the paper is a general convergence theorem for the viscosity solutions of singular perturbation problems for fully nonlinear degenerate parabolic pdes partial differential equations with highly oscillating initial data it substantially generalizes some results obtained previously in 2 under the only assumptions that the hamiltonian is ergodic and stabilizing in a suitable sense the solutions are proved to converge in a relaxed sense to the solution of a limit cauchy problem with appropriate effective hamiltonian and initial data in its formulation our convergence result is analogous to the stability property of barles and perthame it should thus reveal a useful tool for studying general singular perturbation problems by viscosity solutions techniques a detailed exposition of ergodicity and stabilization is given with many examples applications to homogenization and averaging are also discussed

large time asymptotics for one dimensional dirichlet problems for hamilton jacobi equations with noncoercive hamiltonians we study large time asymptotics for a class of noncoercive hamilton jacobi equations with dirichlet boundary condition in one space dimension we prove that the average growth rate of a solution is constant only in a subset of the whole domain and give the asymptotic profile in the subset we show that the large time behavior for noncoercive problems may depend on the space variable in general which is different from the usual results under the coercivity condition this work is an extension with more rigorous analysis of a recent paper by e yokoyama y giga and p rybka in which a growing crystal model is established and the asymptotic behavior described above is first discovered

some simultaneous iterations for finding all zeros of a polynomial with high order convergence in this paper using lagrange interpolation with special nodes we construct some iterations for simultaneously finding all zeros of an algebraic polynomial with high order convergence

the perturbed test function method for viscosity solutions of nonlinear pde the method of viscosity solutions for nonlinear partial differential equations pdes justifies passages to limits by in effect using the maximum principle to convert to the corresponding limit problem for smooth test functions we describe in this paper a perturbed test function device which entails various modifications of the test functions by lower order correctors applications include homogenisation for quasilinear elliptic pdes and approximation of quasilinear parabolic pdes by systems of hamilton jacobi equations

fully nonlinear neumann type boundary conditions for first order hamilton jacobi equations we consider problems of the following type h x u u 0 in where is a smooth bounded open set in r n u is a scalar function from into r u denotes its frechet differential at x and h is a given continuous function on xr r n this equation is nothing but a general form of the classical first order hamilton jacobi equation in order to investigate existence and uniqueness questions the equation has to be complemented with a boundary condition on or on a part of we consider here for reasons described below a fully nonlinear boundary condition of the form f x u u 0 on that we describe as being of the neumann type

stochastic homogenization of hamilton jacobi bellman equations we study the homogenization of some hamilton jacobi bellman equations with a vanishing second order term in a stationary ergodic random medium under the hyperbolic scaling of time and space imposing certain convexity growth and regularity assumptions on the hamiltonian we show the locally uniform convergence of solutions of such equations to the solution of a deterministic effective first order hamilton jacobi equation the effective hamiltonian is obtained from the original stochastic hamiltonian by a minimax formula our homogenization results have a large deviations interpretation for a diffusion in a random environment c 2006 wiley periodicals inc

hamilton jacobi equations in infinite dimensions i uniqueness of viscosity solutions soient un espace de banach v son dual v et des solutions d une equation h x u du 0 dans etablies dans un sous ensemble de v h v r v r est continue on demontre que des solutions classiques sont determinees de facon unique par leurs valeurs limites on montre que l extension de la notion de solutions viscosite aux espaces de banach reussit dans des espaces munis de la propriete de radon nikodym

on cell problems for hamilton jacobi equations with non coercive hamiltonians and their application to homogenization problems abstract we study a cell problem arising in homogenization for a hamilton jacobi equation whose hamiltonian is not coercive we introduce a generalized notion of effective hamiltonians by approximating the equation and characterize the solvability of the cell problem in terms of the generalized effective hamiltonian under some sufficient conditions the result is applied to the associated homogenization problem we also show that homogenization for non coercive equations fails in general

stochastic homogenization of interfaces moving with changing sign velocity abstract we are interested in the averaging behavior of interfaces moving in stationary ergodic environments with oscillatory normal velocity which changes sign the problem can be reformulated as the homogenization of a hamilton jacobi equation with a positively homogeneous of degree one non coercive hamiltonian the periodic setting was studied earlier by cardaliaguet lions and souganidis 2009 16 here we concentrate in the random media and show that the solutions of the oscillatory hamilton jacobi equation converge in l weak to a linear combination of the initial datum and the solutions of several initial value problems with deterministic effective hamiltonian s determined by the properties of the random media

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions part i the case of bounded stochastic evolutions on etudie des equations elliptiques degenerees d ordre 2 non lineaires de la forme f d 2 u du u x 0 dans h ou h est un espace de hilbert separable x un point generique dans h u une fonction de h r

a fuzzy set approach to fault tree and reliability analysis abstract conventional fault tree and reliability analysis does not give a picture concerning the tolerances of the probability values of hazards to overcome this shortcoming the relative frequencies of the basic envents are considered as fuzzy numbers using standard approximations for the membership functions n ary possibilistic and or and neg operators are derived allowing a straightforward evaluation of the frequencies of hazard events in complex systems simultaneously with their tolerances the paper shows the use of these operators for constructing possibilistic fault trees the use of the method for numerical calculation is demonstrated on a real like safety problem

homogenization and enhancement for the g equation we consider the so called g equation a level set hamilton jacobi equation used as a sharp interface model for flame propagation perturbed by an oscillatory advection in a spatio temporal periodic environment assuming that the advection has suitably small spatial divergence we prove that as the size of the oscillations diminishes the solutions homogenize average out and converge to the solution of an effective anisotropic first order spatio temporal homogeneous level set equation moreover we obtain a rate of convergence and show that under certain conditions the averaging enhances the velocity of the underlying front we also prove that at scale one the level sets of the solutions of the oscillatory problem converge at long times to the wulff shape associated with the effective hamiltonian finally we also consider advection depending on position at the integral scale

approximate zeros of quadratically convergent algorithms smale s condition for a point to be an approximate zero of a func tion for newton s method is extended to the general quadratically convergent iterative algorithm it is shown in which way the bound in the condition is affected by the characteristics of the algorithm this puts the original condition of smale for newton s method in a more general perspective the results are also discussed in the light of numerical evidence

hamilton jacobi equations with state constraints in the present paper we consider hamilton jacobi equations of the form h x u vu 0 x e q where q is a bounded open subset of rn h is a given continuous real valued function of x s p e q x r x rn and vu is the gradient of the unknown function u we are interested in particular solutions of the above equation which are required to be supersolutions in a suitable weak sense of the same equation up to the boundary of q this requirement plays the role of a boundary condition the main motivation for this kind of solution comes from deterministic optimal control and differential games problems with constraints on the state of the system as well from related questions in constrained geodesics

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions iii uniqueness of viscosity solutions for general second order equations we prove here the uniqueness and existence of viscosity solutions for a general class of fully nonlinear second order equations in an infinite dimensional hilbert space the uniqueness is proved using the so called inf and sup convolutions which allow some reduction to finite dimensional problems

homogenization for stochastic hamilton jacobi equations homogenization asks whether average behavior can be discerned from partial differential equations that are subject to high frequency fluctuations when those fluctuations result from a dependence on two widely separated spatial scales we prove homogenization for certain stochastic hamilton jacobi partial differential equations the idea is to use the subadditive ergodic theorem to establish the existence of an average in the infinite scale separation limit in some cases we also establish a central limit theorem

a regularity result for viscosity solutions of hamilton jacobi equations in one space dimension on demontre que dans le cas particulier d un probleme stationnaire a une dimension sous des hypotheses tres generales les solutions viscosite continues de lipschitz ont des derivees a droite et a gauche en chaque point

weakly coupled mean field game systems abstract here we prove the existence of solutions to first order mean field games mfgs arising in optimal switching first we use the penalization method to construct approximate solutions then we prove uniform estimates for the penalized problem finally by a limiting procedure we obtain solutions to the mfg problem

viscosity solutions of hamilton jacobi equations with unbounded nonlinear terms abstract the aim of this paper is to introduce a new definition of viscosity solutions for hamilton jacobi equations in infinite dimensions with unbounded nonlinear terms we prove existence and uniqueness results under usual assumptions regarding the bounded part of the hamiltonian

large time behavior of solutions of hamilton jacobi equations with periodic boundary data abstract we study the large time behavior of viscosity solutions of hamilton jacobi equations with periodic boundary data on bounded domains we establish a result on convergence of viscosity solutions to state constraint asymptotic solutions or periodic asymptotic solutions depending on the sign of critical value as time goes to infinity

effective hamiltonians and averaging for hamiltonian dynamics i this paper building upon ideas of mather moser fathi e and others applies pde partial differential equation methods to understand the structure of certain hamiltonian flows the main point is that the cell or corrector pde introduced and solved in a weak sense by lions papanicolaou and varadhan in their study of periodic homogenization for hamilton jacobi equations formally induces a canonical change of variables in terms of which the dynamics are trivial we investigate to what extent this observation can be made rigorous in the case that the hamiltonian is strictly convex in the momenta given that the relevant pde does not usually in fact admit a smooth solution

neumann type boundary conditions for hamilton jacobi equations abstract in this paper we present a notion of viscosity solutions of hamilton jacobi equations for neumann type boundary conditions or more generally oblique derivative in particular we prove the existence uniqueness stability of such solutions and we show that the vanishing viscosity method yields such solutions next we check that value functions of control problems or differential games problems for reflected dynamical processes are solutions in that sense of the associated bellman or isaacs equations finally we consider the ergodic problems

uncertainty in fault tree analysis a fuzzy approach abstract in fault tree analysis the uncertainties in the failure probability and or failure rate of system components or basic events can be propagated to find the uncertainty in the overall system failure probability the conventional approach is monte carlo simulation by assuming a probability distribution for the failure probability in addition a new methodology based on fuzzy set theory is also being used in the fault tree analysis for quantifying the basic event uncertainty and for propagating it however identification of the components which contribute maximum to the system failure probability is also important in fault tree analysis similarly ranking the components based on their contribution of uncertainty to the uncertainty of the system failure probability is also very important this paper presents a comparative study of probabilistic and fuzzy methodologies for top event uncertainty evaluation further it explains a new approach to rank the system components or basic events depending on 1 their contribution to the top event failure probability and 2 their uncertainty contribution to the uncertainty of the top event based on fuzzy set theory

system failure engineering and fuzzy methodology an introductory overview abstract system failure engineering may encompass reliability safety security maintainability risk and quality control in this paper we pay a unified view i e a failure oriented view to system failure engineering the notion of failure can be represented in terms of fuzzy sets and widely interpreted we then discuss various application aspects of fuzzy methodology in system failure engineering which include fuzzy methodology in fault diagnosis in probist systems in structural reliability in software reliability in human reliability in safety engineering in security engineering in risk engineering and in quality control as well as profust posbist and posfust reliability theories engineering case studies and mathematical problems raised by applications of fuzzy methodology in system failure engineering are also addressed in this paper

the theory of smale s point estimation and its applications abstract the main result of this paper is that we exact smale s point estimation theory i e without assuming k p z 1 p k z k k 2 being bounded by the point estimation convergence theorem of the ne method is set up by making use of the majorizing method the proof of the theorem is simple and precise while the required point estimation conditions are weaker than all those of known point estimation convergence theorems another result of this paper is an application of the above new theory to the durand kerner method we compare the point estimation conditions for the durand kerner method with other known point estimation conditions numerical results show that our results have evident advantages

optimal control with state space constraint i optimal control of piecewise deterministic processes with state space constraint is studied under appropriate assumptions it is shown that the optimal value function is the only viscosity solution on the open domain which is also a supersolution on the closed domain finally the uniform continuity of the value function is obtained under a condition on the deterministic drift

weakly coupled systems of the infinity laplace equations we derive the weakly coupled systems of the infinity laplace equations via a tug of war game introduced by peres schramm sheffield and wilson 2009 we establish existence uniqueness results of the solutions and introduce a new notion of generalized cones for systems by using generalized cones we analyze blow up limits of solutions

on advanced computing with words using the generalized extension principle for type 1 fuzzy sets in this paper we propose and demonstrate an effective methodology for implementing the generalized extension principle to solve advanced computing with words acww problems such problems involve implicit assignments of linguistic truth probability and possibility to begin we establish the vocabularies of the words involved in the problems and then collect data from subjects about the words after which fuzzy set models for the words are obtained by using the interval approach ia or the enhanced interval approach eia next the solutions of the acww problems which involve the fuzzy set models of the words are formulated using the generalized extension principle because the solutions to those problems involve complicated functional optimization problems that cannot be solved analytically we then develop a numerical method for their solution finally the resulting fuzzy set solutions are decoded into natural language words using jaccard s similarity measure we explain how acww problems can solve some potential prototype engineering problems and connect the methodology of this paper with perceptual computing

on the guaranteed convergence of the square root iteration method the construction of initial conditions which guarantee the convergence of the applied iterative method is one of the most important problems in solving nonlinear equations which attracted the great attention for many years in this paper we give a precise convergent analysis of the ostrowski like method of the fourth order for the simultaneous determination of polynomial zeros using a procedure based on smale s point estimation theory and some recent results related to the localization of complex polynomial zeros we state initial conditions which enable both the guaranteed and fast convergence of this method these conditions are computationally verifiable since they depend only on polynomial coefficients its degree and initial approximations which is of practical importance

exit time problems in optimal control and vanishing viscosity method the authors study the connections between deterministic exit time control problems and possibly discontinuous viscosity solutions of a first order hamilton jacobi hj equation up to the boundary this equation admits a maximum and a minimum solution that are the value functions associated to stopping time problems on the boundary when these solutions are equal they can be obtained through the vanishing viscosity method finally when the hj equation has a continuous solution it is proved to be the value function for the first exit time of the domain it is also the vanishing viscosity limit arising in particular in some large deviations problems

viscosity solutions for weakly coupled systems of hamilton jacobi equations we obtain comparison results for viscosity solutions of weakly coupled systems of hamilton jacobi equations perron s method is extended to give existence proofs for systems a stronger definition of sub and supersolutions is introduced leading to existence results for continuous solutions the needed sub and supersolutions are constructed for continuous boundary data crandall s and lions notion of viscosity solutions for first order hamilton jacobi equations can be extended in a componentwise way to systems a key tool in obtaining uniqueness comparison and existence results is the maximum principle we obtain such results for weakly coupled systems of hamilton jacobi equations in which the coupling has such a structure to allow the use of maximum principle techniques to motivate the coupling assumptions consider this linear system n

a microscopic time scale approximation to the behavior of the local slope on the faceted surface under a nonuniformity in supersaturation abstract the morphological stability of a growing faceted crystal is discussed we argue that the interplay between nonuniformity in supersaturation on a growing facet and anisotropy of surface kinetics derived from the lateral motion of steps leads to a faceted instability qualitatively speaking as long as the nonuniformity in supersaturation on the facet is not too large it can be compensated for by a variation of step density along the facet and the faceted crystal can grow in a stable manner the problem can be modeled as a hamilton jacobi equation for height of the crystal surface the notion of a maximal stable region of a growing facet is introduced for microscopic time scale approximation of the original hamilton jacobi equation it is shown that the maximal stable region keeps its shape determined by profile of the surface supersaturation with constant growth rate by studying large time behavior of solution of macroscopic time scale approximation a quantitative criterion for the facet stability is given

long time behavior of solutions of hamilton jacobi equations with convex and coercive hamiltonians we investigate the long time behavior of viscosity solutions of hamilton jacobi equations in mathbb r n with convex and coercive hamiltonians and give three general criteria for the convergence of solutions to asymptotic solutions as time goes to infinity we apply the criteria to obtain more specific sufficient conditions for the convergence to asymptotic solutions and then examine them with examples we take a dynamical approach based on tools from weak kam theory such as extremal curves aubry sets and representation formulas for solutions for these investigations

continuous dependence estimates and homogenization of quasi monotone systems of fully nonlinear second order parabolic equations abstract the aim of this paper is to extend the continuous dependence estimates proved by jakobsen and karlsen 2002 3 to quasi monotone systems of fully nonlinear second order parabolic equations as a by product of these estimates we get an holder estimate for bounded solutions of systems and a rate of convergence estimate for the vanishing viscosity approximation in the second part of the paper we employ similar techniques to study the periodic homogenization of quasi monotone systems of fully nonlinear second order uniformly parabolic equations finally some examples are discussed