homogenization of some degenerate pseudoparabolic variational inequalities abstract multiscale analysis of a degenerate pseudoparabolic variational inequality modelling the two phase flow with dynamical capillary pressure in a perforated domain is the main topic of this work regularisation and penalty operator methods are applied to show the existence of a solution of the nonlinear degenerate pseudoparabolic variational inequality defined in a domain with microscopic perforations as well as to derive a priori estimates for solutions of the microscopic problem the main challenge is the derivation of a priori estimates for solutions of the variational inequality uniformly with respect to the regularisation parameter and to the small parameter defining the scale of the microstructure the method of two scale convergence is used to derive the corresponding macroscopic obstacle problem

degradation in common dynamic environments abstractdegradation studies are often used to assess reliability of products subject to degradation induced soft failures because of limited test resources several test subjects may have to share a test rig and have their degradation measured by the same operator the common environments experienced by subjects in the same group introduce significant interindividual correlations in their degradation which is known as the block effect in the present article the wiener process is used to model product degradation and the group specific random environments are captured using a stochastic time scale both semiparametric and parametric estimation procedures are developed for the model maximum likelihood estimations of the model parameters for both the semiparametric and parametric models are obtained with the help of the em algorithm performance of the maximum likelihood estimators is validated through large sample asymptotics and small sample simulations the proposed models are illustrated by an appl

a relaxation procedure for domain decomposition methods using finite elements we present the convergence analysis of a new domain decomposition technique for finite element approximations this technique was introduced in 11 and is based on an iterative procedure among subdomains in which transmission conditions at interfaces are taken into account partly in one subdomain and partly in its adjacent no global preconditioner is needed in the practice but simply single domain finite element solvers are required an optimal strategy for an automatic selection of a relaxation parameter to be used at interface subdomains is indicated applications are given to both elliptic equations and incompressible stokes equations

an inverse gaussian process model for degradation data this paper studies the maximum likelihood estimation of a class of inverse gaussian process models for degradation data both the subject to subject heterogeneity and covariate information can be incorporated into the model in a natural way the em algorithm is used to obtain the maximum likelihood estimators of the unknown parameters and the bootstrap is used to assess the variability of the maximum likelihood estimators simulations are used to validate the method the model is fitted to laser data and corresponding goodness of fit tests are carried out failure time distributions in terms of degradation level passages are calculated and illustrated the supplemental materials for this article are available online

analysis of a darcy flow model with a dynamic pressure saturation relation we consider a new model for groundwater flow the model differs from previous models in that the saturation pressure relation is extended with a dynamic term namely the time derivative of the saturation the resulting model equation is of nonlinear degenerate pseudoparabolic type we give a rigorous analysis of travelling wave solutions and the local behavior near fronts part of this analysis is then used in a formal asymptotic analysis of solutions with initial support in a half line as an illustrative special case we also consider heaviside initial data

optimum allocation rule for accelerated degradation tests with a class of exponential dispersion degradation models optimum allocation problem in accelerated degradation tests adts is an important task for reliability analysts several researchers have attempted to address this decision problem but their results have been based only on specific degradation models therefore they lack a unified approach toward general degradation models this study proposes a class of exponential dispersion ed degradation models to overcome this difficulty assuming that the underlying degradation path comes from the ed class we analytically derive the optimum allocation rules by minimizing the asymptotic variance of the estimated q quantile of product s lifetime for two level and three level adt allocation problems whether the testing stress levels are prefixed or not for a three level allocation problem we show that all test units should be allocated into two out of three stresses depending on certain specific conditions two examples are used to illustrate the proposed procedure furthermore the penalties of using nonopt

small and waiting time behavior of a darcy flow model with a dynamic pressure saturation relation we address the small time evolution of interfaces fronts for the pseudoparabolic generalization partial u over partial t partial over partial x left u alpha partial u over partial x u beta partial 2 u over partial x partial t right of the porous medium equation identifying regimes in which the local behavior remains fixed for some finite time and others in which it changes instantaneously a number of phenomena beyond those exhibited by the porous medium equation are elucidated including retreating fronts and novel types of local behavior related results for the important limit case partial u over partial t partial over partial x left u beta partial 2 u over partial x partial t right are also described

existence of weak solutions for a nonlocal pseudo parabolic model for brinkman two phase flow in asymptotically flat porous media abstract we study a nonlocal evolution equation that involves a pseudo parabolic third order term the equation models almost uni directional two phase flow in brinkman regimes we prove the existence of weak solutions for this equation we also give a series of numerical examples that demonstrate the ability of the equation to support overshooting like in 26 and explore the behavior of solutions in various limit regimes

the richards equation with hysteresis and degenerate capillary pressure abstract we study the richards equation with a dynamic capillary pressure including hysteresis we provide existence and approximation results for degenerate capillary pressure curves p c treating two cases in the first case the permeability function k can be degenerate but the initial saturation does not take the critical values in the second case the permeability function k is strictly positive but the capillary pressure function can be multi valued in both cases the degenerate behavior of p c leads to the physically desired uniform bounds for the saturation variable our approach exploits maximum principles and relies on the corresponding uniform bounds for pressure and saturation a new compactness result for the saturation variable allows to take limits in nonlinear terms the solution concept uses tools of convex analysis

student t processes for degradation analysis stochastic processes are widely used to analyze degradation data and the gaussian process is a particularly common one in this article we propose a robust statistical model using a student t pro

numerical analysis of a finite volume scheme for two incompressible phase flow with dynamic capillary pressure abstract in this paper we propose and analyze the convergence of a tpfa two points flux approximation finite volume scheme to approximate the two incompressible phase flow with dynamic capillary pressure in porous media the fully implicit scheme is based on nonstandard approximation on mobilities and capillary pressure on the dual mesh we derive a discrete variational formulation and we present a new result of convergence in a two or three dimensional porous medium in comparison with static capillary pressure the non equilibrium capillary model requires more powerful techniques especially the discrete energy estimates are not standard

degenerate quasilinear pseudoparabolic equations with memory terms and variational inequalities abstract the existence of solutions of degenerate quasilinear pseudoparabolic equations where the term t u is replace by t b u with memory terms and quasilinear variational inequalities is shown the existence of solutions of equations is proved under the assumption that the nonlinear function b is monotone and a gradient of a convex continuously differentiable function the uniqueness is proved for lipschitz continuous elliptic parts the existence of solutions of quasilinear variational inequalities is proved under stronger assumptions namely the nonlinear function defining the elliptic part is assumed to be a gradient and the function b to be lipschitz continuous

central extensions of sn as galois groups of regular extensions of q t recently mestre me has proved that the double cover a of the alternating group a is realizable as the galois group of a regular extension of the rational function field uj t for all ii 3 4 we show here that his method yields the same result for the two double covers s of the symmetric group s z and more generally for every finite central extension of s partial results on s have been obtained previously by several authors kss sol so2 ss v

stable patterns in a viscous diffusion equation we consider a pseudoparabolic regularization of a forward backward nonlinear diffusion equation ut a f u vut motivated by the problem of phase separation in a viscous binary mixture the function f is nonmonotone so there are discontinuous steady state solutions corresponding to arbitrary arrangements of phases we find that any bounded measurable steady state solution u x satisfying f u constant f u x 0 a e is dynamically stable to perturbations in the sense of convergence in measure in particular smooth solutions may achieve discontinuous asymptotic states furthermore stable states need not correspond to absolute minimizers of free energy thus violating gibbs principle of stability for phase mixtures

a model problem for groundwater flow with dynamic capillary pressure stability of travelling waves modelling vertical nonsteady groundwater flow with dynamic capillary pressure leads to a nonlinear diffusion convection equation extended with a nonlinear third order term with two space derivatives and one time derivative we consider the special case in which the original equation is the burgers equation and the third order term is linear we investigate stability of travelling wave solutions of the resulting pseudo parabolic burgers equation for which we first obtain well posedness results

finite element galerkin method for 2d sobolev equations with burgers type nonlinearity abstract in this article the global existence of a unique strong solution to the 2d sobolev equation with burgers type nonlinearity is established using weak or weak compactness type arguments when the forcing function f 0 is in l l2 new a priori bounds are derived which are valid uniformly in time as t and with respect to the dispersion coefficient as 0 it is further shown that the solution of the sobolev equation converges to the solution of the 2d burgers equation with order o a finite element method is applied to approximate the solution in the spatial direction and the existence of a global attractor is derived for the semidiscrete scheme further using a priori bounds and an integral operator optimal error estimates are derived in l l2 norm which hold uniformly with respect to as 0 since the constants in the error estimates have exponential growth in time therefore under a certain uniqueness condition the error bounds are derived which are uniformly in time more importantly all the above results remain valid as tends to zero finally this paper concludes with some numerical examples

models for variable stress accelerated life testing experiments based on wiener processes and the inverse gaussian distribution variable stress accelerated life testing trials are experiments in which each of the units in a random sample of units of a product is run under increasingly severe conditions to get information quickly on its life distribution we consider a fatigue failure model in which accumulated decay is governed by a continuous gaussian process w y whose distribution changes at certain stress change points to t l t k continuously increasing stress is also considered failure occurs the first time w y crosses a critical boundary the distribution of time to failure for the models can be represented in terms of time transformed inverse gaussian distribution functions and the parameters in models for experiments with censored data can be estimated using maximum likelihood methods a common approach to the modeling of failure times for experimental units subject to increased stress at certain stress change points is to assume that the failure times follow a distribution that consists of segments of weib

a global existence result for the equations describing unsaturated flow in porous media with dynamic capillary pressure in this paper we investigate the pseudoparabolic equation tc div k c pc c c tc g en where is a positive constant c is the moisture content k is the hydraulic conductivity and pc is the static capillary pressure this equation describes unsaturated flows in porous media with dynamic capillary pressure saturation relationship in general such models arise in a number of cases when non equilibrium thermodynamics or extended non equilibrium thermodynamics are used to compute the flux for this equation existence of the traveling wave type solutions was extensively studied nevertheless the existence seems to be known only for the non degenerate case when k is strictly positive we use the approach from statistical hydrodynamics and construct the corresponding entropy functional for the regularized problem such approach permits to get existence for any time interval of an appropriate weak solution with square integrable first derivatives in x and in t and square integrable time derivative of the gradient negative part of such weak solution is small in l2 norm with respect to x uniformly in time as the square root of the relative permeability at the value of the regularization parameter next we control the regularized entropy a fine balance between the regularized entropy and the degeneracy of the capillary pressure permits to get an lq uniform bound for the time derivative of the gradient these estimates permit passing to the limit when the regularization parameter tends to zero and obtaining the existence of global nonnegative weak solution

blow up phenomena for a pseudo parabolic equation with p laplacian and logarithmic nonlinearity terms abstract this paper deals with a pseudo parabolic equation with p laplacian and logarithmic nonlinearity terms under homogeneous dirichlet boundary condition in a smooth bounded domain which was studied in 12 and the global existence and finite time blow up of the weak solution were studied under different energy levels we generalize and extend those results by discussing the asymptotic behavior of the weak solution and proving that the weak solution converges to the corresponding stationary solution as time tends to infinity moreover a lower and an upper bound estimation for blow up time and rate are obtained for the blow up weak solution in different initial energy cases furthermore we establish the weak solution with high initial energy that is global bounded or blow up under some sufficient conditions as well as a nonblow up criterion and algebraic decay result in other assumptions

generalized nonequilibrium capillary relations for two phase flow through heterogeneous media for two phase flow in porous media the natural medium heterogeneity necessarily gives rise to capillary nonequilibrium effects the relaxation to the equilibrium is a slow process which should be introduced in macroscopic flow models many nonequilibrium models are based on a phenomenological approach at the same time there exists a rigorous mathematical way to develop the nonequilibrium equations its formalism developed by bourgeat and panfilov computational geosciences 2 191 1998 is based on the homogenization of the microscale flow equations over medium heterogeneities in contrast with the mentioned paper in which the case of a sufficiently fast relaxation was analyzed we consider the case of long relaxation which leads to the appearance of long term memory on the macroscale due to coupling between the nonlinearity and nonlocality in time the macroscopic model remains however incompletely homogenized in the general case at the same time frequently only the relationship for the nonequilibrium capillary pressure is of interest for applications in the present paper we obtain such an exact relationship in two different independent forms for the case of long term memory this relationship is more general than that obtained by bourgeat and panfilov in addition we prove the comparison theorem which determines the upper and lower bounds for the macroscopic model these bounds represent linear flow models which are completely homogenized the results obtained are illustrated by numerical simulations

a time discrete and zero adjusted gamma process model with application to degradation analysis abstract the standard gamma process is widely used for degradation modelling when the degradation paths are always positive and strictly increasing nevertheless the standard gamma process is considered inappropriate if the observed sample paths are horizontal over several time intervals motivated by this phenomenon we develop a time discrete and zero adjusted gamma process model statistical inference method of this model is then proposed to illustrate our proposed model both simulation study and real data analysis are conducted whose results demonstrate that the proposed model has satisfactory fit performance and predictive performance

double covers of s5 and frobenius groups as galois groups over number fields abstract it is proved that the two double covers of s 5 are galois groups over every number field this together with same result for the double cover of a 5 proved by feit yields the result that every frobenius group is a galois group over every number field

condition based maintenance using the inverse gaussian degradation model abstract condition based maintenance has been proven effective in reducing unexpected failures with minimum operational costs this study considers an optimal condition based replacement policy with optimal inspection interval when the degradation conforms to an inverse gaussian process with random effects the random effects parameter is used to account for heterogeneities commonly observed among a product population its distribution is updated when more degradation observations are available the observed degradation level together with the unit s age are used for the replacement decision the structure of the optimal replacement policy is investigated in depth we prove that the monotone control limit policy is optimal we also provide numerical studies to validate our results and conduct sensitivity analysis of the model parameters on the optimal policy

the unsaturated flow in porous media with dynamic capillary pressure abstract in this paper we consider a degenerate pseudoparabolic equation for the wetting saturation of an unsaturated two phase flow in porous media with dynamic capillary pressure saturation relationship where the relaxation parameter depends on the saturation following the approach given in 13 the existence of a weak solution is proved using galerkin approximation and regularization techniques a priori estimates needed for passing to the limit when the regularization parameter goes to zero are obtained by using appropriate test functions motivated by the fact that considered pde allows a natural generalization of the classical kullback entropy finally a special care was given in obtaining an estimate of the mixed derivative term by combining the information from the capillary pressure with the obtained a priori estimates on the saturation

two phase porous media flows with dynamic capillary effects and hysteresis in this paper we obtain the uniqueness of weak solutions for a two phase flow model in a porous medium a particularity of the model is that the dynamic effects and hysteresis are included in the capillary pressure to prove the uniqueness we define an auxiliary elliptic system

numerical investigations of two phase flow with dynamic capillary pressure in porous media via a moving mesh method abstract motivated by observations of saturation overshoot this paper investigates numerical modeling of two phase flow in porous media incorporating dynamic capillary pressure the effects of the dynamic capillary coefficient the infiltrating flux rate and the initial and boundary values are systematically studied using a traveling wave ansatz and efficient numerical methods the traveling wave solutions may exhibit monotonic non monotonic or plateau shaped behavior special attention is paid to the non monotonic profiles the traveling wave results are confirmed by numerically solving the partial differential equation using an accurate adaptive moving mesh solver comparisons between the computed solutions using the brooks corey model and the laboratory measurements of saturation overshoot verify the effectiveness of our approach

error estimates for a mixed finite element discretization of a two phase porous media flow model with dynamic capillarity abstract we analyze a fully discrete numerical scheme for the model describing two phase immiscible flow in porous media with dynamic effects in the capillary pressure we employ the euler implicit method for the time discretization the spatial discretization is based on the mixed finite element method mfem specifically the lowest order raviart thomas elements are applied in this paper the error estimates for the saturation fluxes and phase pressures in l 0 t l 2 are derived for the temporal and spatial discretization to show the convergence of the scheme finally we present some numerical results to support the theoretical findings

global solution and blow up for a class of pseudo p laplacian evolution equations with logarithmic nonlinearity the main goal of this work is to study an initialboundary value problem for a nonlinear pseudoparabolic equation with logarithmic nonlinearity by using the potential well method and a logarithmic sobolev inequality we obtain results of existence or nonexistence of global weak solutions in addition we also provide sufficient conditions for the large time decay of global weak solutions and the finite time blow up of weak solutions

central extensions of symmetric groups as galois groups supported in part by the wolf foundation supported in part by nsf grant dms85 00929 during this work murray schacher was also a fulbright hayes fellow in belgium under the auspices of the commission for educational exchange between the united states belgium and luxembourg

the inverse gaussian process as a degradation model this article systematically investigates the inverse gaussian ig process as an effective degradation model the ig process is shown to be a limiting compound poisson process which gives it a meaningful physical interpretation for modeling degradation of products deteriorating in random environments treated as the first passage process of a wiener process the ig process is flexible in incorporating random effects and explanatory variables that account for heterogeneities commonly observed in degradation problems this flexibility makes the class of ig process models much more attractive compared with the gamma process which has been thoroughly investigated in the literature of degradation modeling the article also discusses statistical inference for three random effects models and model selection it concludes with a real world example to demonstrate the applicability of the ig process in degradation analysis supplementary materials for this article are available online

semiparametric estimation of gamma processes for deteriorating products this article investigates the semiparametric inference of the simple gamma process model and a random effects variant maximum likelihood estimates of the parameters are obtained through the em algorithm the bootstrap is used to construct confidence intervals a simulation study reveals that an estimation based on the full likelihood method is more efficient than the pseudo likelihood method in addition a score test is developed to examine the existence of random effects under the semiparametric scenario a comparison study using a fatigue crack growth dataset shows that performance of a semiparametric estimation is comparable to the parametric counterpart this article has supplementary material online

on convergence of a discrete problem describing transport processes in the pressing section of a paper machine including dynamic capillary effects one dimensional case this work presents a proof of convergence of a discrete solution to a continuous one at first the continuous problem is stated as a system of equations which describe the filtration process in the pressing section of a paper machine two flow regimes appear in the modeling of this problem the model for the saturated flow is presented by the darcy s law and the mass conservation the second regime is described by the richards approach together with a dynamic capillary pressure model the finite volume method is used to approximate the system of pdes then the existence of a discrete solution to the proposed finite difference scheme is proven compactness of the set of all discrete solutions for different mesh sizes is proven the main theorem shows that the discrete solution converges to the solution of the continuous problem at the end we present numerical studies for the rate of convergence

equivalent formulations and numerical schemes for a class of pseudo parabolic equations this paper investigates three different formulations for a class of pseudo parabolic equations such equations are encountered for example as a model for two phase porous media flows when dynamic effects in the capillary pressure are included we first show the equivalence of the three different formulations for the original equation on the basis of this we further investigate the corresponding discretization in time and give some numerical examples

degenerate two phase porous media flow model with dynamic capillarity abstract in this paper we investigate a degenerate elliptic parabolic system which describes the flow of two incompressible immiscible fluids in porous media and including dynamic effects in the phase pressure difference first for the regularized case the existence and uniqueness of the weak solution are obtained then we let the regularization parameter go to zero to show the existence of weak solutions under degenerate case

convergence analysis of p1 finite element method for free boundary problems on non overlapping subdomains abstract the paper applies a conforming p1 finite element method to general variational inequalities derived from free boundary problems the domain of the free boundary problem can be properly split into two non overlapping subdomains where the free boundary is located in only one subdomain the variational inequality is reduced to a partial differential equation in the subdomain which does not contain the free boundary but still keeps its original form in the other subdomain therefore the original variational inequality can be discretized separately with p1 finite element in different subdomains a non overlapping domain decomposition method is introduced to solve these two discretized sub problems by p1 finite element method iteratively while a robin type boundary condition is utilized for the data transfer on the common boundary we show that the sequence of such finite element solutions converges to the discretized solution of the original problem application to a free seepage problem verifies the theory

an additive schwarz method for variational inequalities this paper proposes an additive schwarz method for variational inequalities and their approximations by finite element methods the schwarz domain decomposition method is proved to converge with a geometric rate depending on the decomposition of the domain the result is based on an framework of convergence analysis established for general variational inequalities in hilbert spaces

on a class of forward backward parabolic equations formation of singularities abstract we study the formation of singularities for the problem u t u x x e u t x x in 0 t u e u t 0 in 0 t u u 0 0 in 0 where and t are positive constants a bounded interval u 0 a nonnegative radon measure on a nonmonotone and nonnegative function with 0 0 and an increasing bounded function we show that if u 0 is a bounded or continuous function singularities may appear spontaneously the class of singularities which can arise in finite time is remarkably large and includes infinitely many dirac masses and singular continuous measures

analysis of an interior penalty discontinuous galerkin scheme for two phase flow in porous media with dynamic capillary effects we present an interior penalty discontinuous galerkin scheme for a two phase porous media flow model that incorporates dynamic effects in the capillary pressure the approximation of the mass conservation laws is performed in their original formulation without introducing a global pressure we prove the existence of a solution to the emerging fully discrete systems and the convergence of the scheme error estimates are obtained for sufficiently smooth data