weak solutions for an inviscid two phase flow model in physical vacuum abstract we investigate a free boundary problem for the inviscid two phase flow model with moving physical vacuum boundary which is a degenerate and characteristic hyperbolic system of conservation laws based on a suitable transformation a special degenerate parabolic approximation and delicate uniform energy estimates we prove the existence and uniqueness of the local weak solutions this can be regarded as a generalization of the results in coutand and shkoller 2011 5 from single phase gas model to two phase gas liquid model

singular behavior of vacuum states for compressible fluids in this survey paper we will present the recent work on the study of the compressible fluids with vacuum states by illustrating its interesting and singular behavior through some systems of fluid dynamics that is euler equations euler poisson equations and navier stokes equations the main concern is the well posedness of the problem when vacuum presents and the singular behavior of the solution near the interface separating the vacuum and the gas furthermore the relation of the solutions for the gas dynamics with vacuum to those of the boltzmann equation will also be discussed in fact the results obtained so far for vacuum states are far from being complete and satisfactory therefore this paper can only be served as an introduction to this interesting field which has many open and challenging mathematical problems moreover the problems considered here are limited to the author s interest and knowledge in this area

distributivity equation in the class of 2 uninorms this paper is mainly devoted to solving the functional equation of distributivity between aggregation operators with 2 neutral element our investigations are motivated by the couple of distributive logical connectives and their generalizations used in fuzzy set theory e g triangular norms conorms uninorms nullnorms and implications one of the recent generalizations covering both uninorms and nullnorms are 2 uninorms which form a class of commutative associative and increasing operators on the unit interval with an absorbing element separating two subintervals having their own neutral elements in this work the distributivity of two binary operators from the class of 2 uninorms is considered in particular all possible solutions of the distributivity equation for the three defined subclasses of these operators depending on the position of its zero and neutral elements are characterized

convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping we consider a model of hyperbolic conservation laws with damping and show that the solutions tend to those of a nonlinear parabolic equation time asymptotically the hyperbolic model may be viewed as isentropic euler equations with friction term added to the momentum equation to model gas flow through a porous media in this case our result justifies darcy s law time asymptotically our model may also be viewed as an elastic model with damping

on the vacuum state for the equations of isentropic gas dynamics condition c which is dictated by physics is a source of essential difficulties in the mathematical treatment of this problem there have been extensive studies on the smooth solutions for equations e 2 61 these studies are concerned with states p u in the region strictly away from the vacuum that is p l u p0 for some fixed positive constant p a necessary condition for the existence of a global bounded continuous solution is

well posedness of 1 d compressible euler poisson equations with physical vacuum abstract this paper is concerned with the 1 d compressible euler poisson equations with moving physical vacuum boundary condition it is usually used to describe the motion of a self gravitating inviscid gaseous star the local well posedness of classical solutions is established in the case of the adiabatic index 1 3

l 1 convergence to the barenblatt solution for compressible euler equations with damping we study the asymptotic behavior of compressible isentropic flow through a porous medium when the initial mass is finite the model system is the compressible euler equation with frictional damping as t the density is conjectured to obey the well known porous medium equation and the momentum is expected to be formulated by darcy s law in this paper we prove that any l weak entropy solution to the cauchy problem of damped euler equations with finite initial mass converges strongly in the natural l1 topology with decay rates to the barenblatt profile of the porous medium equation the density function tends to the barenblatt solution of the porous medium equation while the momentum is described by darcy s law the results are achieved through a comprehensive entropy analysis capturing the dissipative character of the problem

well posedness in smooth function spaces for moving boundary 1 d compressible euler equations in physical vacuum we prove well posedness for the 3 d compressible euler equations with moving physical vacuum boundary with an equation of state given by the so called gamma gas law for gamma 1 the physical vacuum singularity requires the sound speed c to go to zero as the square root of the distance to the moving boundary and thus creates a degenerate and characteristic hyperbolic free boundary system wherein the density vanishes on the free boundary the uniform kreiss lopatinskii condition is violated and manifest derivative loss ensues nevertheless we are able to establish the existence of unique solutions to this system on a short time interval which are smooth in sobolev spaces all the way to the moving boundary and our estimates have no derivative loss with respect to initial data our proof is founded on an approximation of the euler equations by a degenerate parabolic regularization obtained from a specific choice of a degenerate artificial viscosity term chosen to preserve as much of the geometric structure of the euler equations as possible we first construct solutions to this degenerate parabolic regularization using a new higher order hardy type inequality we then establish estimates for solutions to this degenerate parabolic system which are independent of the artificial viscosity parameter solutions to the compressible euler equations are found in the limit as the artificial viscosity tends to zero our regular solutions can be viewed as degenerate viscosity solutions out methodology can be applied to many other systems of degenerate and characteristic hyperbolic systems of conservation laws

a priori estimates for the free boundary 3d compressible euler equations in physical vacuum we prove a priori estimates for the three dimensional compressible euler equations with moving physical vacuum boundary with an equation of state given by p c for 1 the vacuum condition necessitates the vanishing of the pressure and hence density on the dynamic boundary which creates a degenerate and characteristic hyperbolic free boundary system to which standard methods of symmetrizable hyperbolic equations cannot be applied

migrativity property for uninorms the migrative uninorms over a fixed uninorm with different neutral elements are presented all cases when both uninorms lay in any one of the most usual classes of uninorms are analyzed characterizing all solutions of the migrativity equation for some possible combinations the solutions obtained generalize the results where both uninorms have the same neutral elements

convergence to nonlinear diffusion waves for solutions of p system with time dependent damping abstract in this paper we study the cauchy problem for the hyperbolic p system with time gradually degenerate damping term 1 1 t u for 0 1 and show that the damped p system has a couple of global solutions uniquely and such solutions tend time asymptotically to the shifted nonlinear diffusion waves which are the solutions of the corresponding nonlinear parabolic equation governed by the darcy s law we further derive the convergence rates when the initial perturbations are in l 2 the approach adopted is the technical time weighted energy method

on pure derived categories abstract we investigate the properties of pure derived categories of module categories and show that pure derived categories share many nice properties of classical derived categories in particular we show that bounded pure derived categories can be realized as certain homotopy categories we introduce the pure projective resp injective dimension of complexes in pure derived categories and give some criteria for computing these dimensions in terms of the properties of pure projective resp injective resolutions and pure derived functors as a consequence we get some equivalent characterizations for the finiteness of the pure global dimension of rings finally pure projective resp injective resolutions of unbounded complexes are considered

blowup for the 3d compressible euler equations abstract we establish several results about the blowup of the solutions for the cauchy problem of the 3d compressible euler equations under some assumptions on weighed functionals associated with the initial momentum that they are large enough to develop singularities especially we prove the blowup results without the condition 0 x 0 e s x 0 e s d x 0 while it is an essential condition in the well known result obtained by thomas c sideris

initial boundary value problem of euler equations with damping in r n abstract the asymptotic wave behavior of solution for the euler equations with damping in r n is investigated around a given constant equilibrium in this paper three classical boundary condition cases are considered here new approaches and techniques are introduced to deal with the multi dimensional case for the system for the linearized problem by comparing symbols in the transformed tangential spatial and time space we show that its green s function can be described in terms of the fundamental solution for the cauchy problem and reflected fundamental solution coupled with a boundary operator our approaches help us to simplify the green s function to the essential part and benefit the follow up nonlinear analysis for the nonlinear problem we prove the pointwise decaying rate with the help of the duhamel s principle

strong solutions of the navier stokes equations for isentropic compressible fluids we study strong solutions of the isentropic compressible navier stokes equations in a domain r3 we first prove the local existence of unique strong solutions provided that the initial data 0 and u0 satisfy a natural compatibility condition the important point in this paper is that we allow the initial vacuum the initial density may vanish in an open subset of we then prove a new uniqueness result and stability result our results are valid for unbounded domains as well as bounded ones

l1 convergence rates to the barenblatt solution for the damped compressible euler equations abstract in our previous work 17 it is shown that any l weak entropy solution of damped compressible euler equation converges to the barrenblatt s solution with finite mass in l 1 norm with a convergence rate for 1 3 in this paper by introducing an elaborate iterative method and using the intensive entropy analysis we prove the l 1 convergence to the barrenblatt s solution for any large 3 furthermore we get better l 1 convergence rate for 2 3

on global multidimensional supersonic flows with vacuum states at infinity in this paper we are concerned with the global existence and stability of a smooth supersonic flow with vacuum state at infinity in a three dimensional infinitely long divergent nozzle the flow is described by a three dimensional steady potential equation which is multi dimensional quasilinear hyperbolic but degenerate at infinity with respect to the supersonic direction and whose linearized part admits the form partial t 2 frac 1 1 t 2 gamma 1 partial 1 2 partial 2 2 frac 2 gamma 1 1 t partial t for 1 gamma 2 from the physical point of view due to the expansive geometric property of the divergent nozzle and the mass conservation of gases the moving gases in the nozzle will gradually become rarefactive and tend to vacuum states at infinity which implies that such a smooth supersonic flow should be globally stable for small perturbations since there are no strong resulting compressions in the motion of the flow we will confirm such a global stability phenomenon by rigorous mathematical proofs and further show that there do not exist vacuum domains in any finite parts of the nozzle

the derived category of an exact category there is some confusion in the literature regarding the derived category of an exact category 8 thomason gives a satisfactory treatment of the bounded derived category in ct 1 11 6 see also appendix a the result is that provided all weakly split epimorphisms in 8 are admissible the bounded derived category may be defined as usual although thomason does not say it the categories d 6 d d may also be defined in the same way the definition of the unbounded derived category is more difficult and is very poorly treated in the literature for instance in bbd this derived category is only defined provided every morphism in 6 admits a kernel see bbd 1 1 41 this is very unsatisfactory since very few exact categories satisfy the condition in this article we will show that d b may be defined whenever 6 is saturated karoubian in thomason s terminology an exact category is saturated if every idempotent splits i e 6 contains all direct summands of its objects for the purpose of comparing with thomason s result the bounded derived category is defined for more 8 s all that is required to define db is that whenever an idempotent e a a factors as a f ba a with fog lb then e is split thomason calls such idempotents weakly split and we will honor his notation we will show here that these constructions are in some sense best possible remark 1 8 for d 6 remarks 1 9 and 1 10 for d d d b db 6 there are two reasons why i wrote this note one is to correct the misconceptions in the literature but more importantly the proof of the key result lemma 1 2 depends on an important characterization of tpaisse subcategories due to rickard and this article is intended to highlight rickard s criterion a full triangulated subcategory y of a triangulated

stabilities for euler poisson equations in some special dimensions abstract we study the stabilities and classical solutions of euler poisson equations describing the evolution of the gaseous star in astrophysics in fact we extend the study of the stabilities of euler poisson equations with or without frictional damping term to some special dimensional spaces besides by using the second inertia function in 2 dimension of euler poisson equations we prove the non global existence of classical solutions with 2 u 2 2 p d x g m 2 for any

initial boundary value problem for p system with damping in half space abstract in this paper the initial boundary value problem for p system with damping in half space is studied with a posed mix boundary condition the fundamental solution green s function for cauchy problem is constructed with a sharp decaying structure and a precise capture of the singularity by a singularity removal process later the symbols of both fundamental solution and green s function for initial boundary value problem are obtained with transformed variable s and spatial variable x while in this level the green s function could be decomposed into fundamental solution and boundary operator thus with the study of boundary operator and previous precise information about the fundamental solution the pointwise structure as well as the singular structure of the green s function is established finally the nonlinear stability is obtained by the green s function and a priori estimate from energy method

global existence of spherically symmetric solutions for nonlinear compressible navier stokes equations this paper concerns the global existence of solutions in hi i 1 2 4 for the nonlinear compressible navier stokes equations of an initial boundary value problem with an external force and a heat source some important inequalities are used and some new results are obtained

restricted distributivity for aggregation operators with absorbing element the problem of restricted distributivity i e a form of relaxed distributivity on the restricted domain plays an important role in many different fields such as utility theory and integration theory this paper considers the following two cases of restricted distributivity i a continuous nullnorm with respect to a continuous t conorm and ii a continuous nullnorm with respect to a uninorm of the form u m i n or u m a x with continuous underlying t norm and t conorm

well posedness in smooth function spaces for the moving boundary three dimensional compressible euler equations in physical vacuum we prove well posedness for the three dimensional compressible euler equations with moving physical vacuum boundary with an equation of state given by p c for 1 the physical vacuum singularity requires the sound speed c to go to zero as the square root of the distance to the moving boundary and thus creates a degenerate and characteristic hyperbolic free boundary system wherein the density vanishes on the free boundary the uniform kreiss lopatinskii condition is violated and manifest derivative loss ensues nevertheless we are able to establish the existence of unique solutions to this system on a short time interval which are smooth in sobolev spaces all the way to the moving boundary and our estimates have no derivative loss with respect to initial data our proof is founded on an approximation of the euler equations by a degenerate parabolic regularization obtained from a specific choice of a degenerate artificial viscosity term chosen to preserve as much of the geometric structure of the euler equations as possible we first construct solutions to this degenerate parabolic regularization using a higher order version of hardy s inequality we then establish estimates for solutions to this degenerate parabolic system which are independent of the artificial viscosity parameter solutions to the compressible euler equations are found in the limit as the artificial viscosity tends to zero our regular solutions can be viewed as degenerate viscosity solutions our methodology can be applied to many other systems of degenerate and characteristic hyperbolic systems of conservation laws

the modularity condition for uninorms revisited abstract functional equations involving aggregation functions play an important role in fuzzy sets and fuzzy logic theory the modularity equation is a kind of restricted general associative equations in the literature the already known results concerning the modularity equation for two uninorms are based on the assumption that both uninorms lie in one of the most studied classes of uninorms in this study we explore the modularity equation involving uninorms in a most general setting specifically we investigate the modularity between two uninorms in the cases when one uninorm belongs to any of the most studied classes of uninorms but the other one is any uninorm with no further assumptions further many new solutions appear from this new point of view that were not included in previous approaches

blowup for irrotational c1 solutions of the compressible euler equations in rn abstract in this article we study the finite life span of the irrotational c 1 non vacuum solutions for the compressible euler equations in r n in fluid dynamics we present the blowup results for the c 1 solutions for which the initial functional h 0 r n x u 0 d v is sufficiently large to partially complement the classical sideris blowup results f 0 r 3 x 0 u 0 d v sideris 1985 our blowup conditions do not depend on the density 0

blowup of the axis symmetric solutions for the ibvp of the isentropic euler equations abstract in this paper we present several results about the blowup of the axis symmetric solutions for the initial boundary value problem of the isentropic euler equations for a perfect gas under some assumptions that the functionals of the initial data are large enough to develop singularities

a note on the modularity law in some classes of aggregation operators abstract in this paper the study of the functional equation of modularity for 2 uninorms recently published by fechner rak and zedam is revisited a result from corollary 6 3 in the mentioned paper is corrected and it is now given in a correct form furthermore we characterize more general cases of modularity for 2 uninorms

well posedness for compressible euler equations with physical vacuum singularity an important problem in the theory of compressible gas flows is to understand the singular behavior of vacuum states the main difficulty lies in the fact that the system becomes degenerate at the vacuum boundary where the characteristic speeds u c coincide and have unbounded spatial derivative since c behaves like x 1 2 close to the boundary in this paper we overcome this difficulty by presenting a new formulation and new energy spaces we establish the local in time well posedness of one dimensional compressible euler equations for isentropic flows with the physical vacuum singularity in some spaces adapted to the singularity 2009 wiley periodicals inc

the modularity condition for uninorms and t operators in this work we study the functional equation given by the modularity condition f x g y z g f x y z for all z x where the unknown functions f g are uninorms and or t operators we characterize all the solutions in the four possible cases i when f g are t operators ii when f is a t operator and g a uninorm iii when f is a uninorm and g a t operator and finally iv when f g are uninorms

stationary solutions to euler equations with spherical symmetry abstract in this paper as a first step to study the large time behavior of solutions to the compressible euler equations on a half line we consider the two classes of compressible euler equations and prove the existence of stationary solutions with spherical symmetry form the aim is to concentrate on understanding the influence of boundary conditions

the modularity condition for semi t operators abstract the aim of this paper is mainly to solve the functional equations given by the modularity condition several years ago the modularity equations were discussed in families of certain commutative operations such as t norms t conorms uninorms 2 uninorms and t operators in this study we continue the investigation of this same topic by focusing on semi t operators which are generalization of t operators by omitting commutativity our results are not only the full characterization of this modularity condition for semi t operators with continuous underlying operators but also generalize the case for t operators under certain conditions

uninorm solutions and or nullnorm solutions to the modularity condition equations in this paper uninorm solutions and or nullnorm solutions to the modularity condition equations are in detail discussed and then we find that no new non trivial solutions to the equations appear where uninorms discussed lie in the set cu of uninorms continuous in 0 1 2 further the differences between elements in cu and in u have been shown

well posedness for the motion of physical vacuum of the three dimensional compressible euler equations with or without self gravitation this paper concerns the well posedness theory of the motion of a physical vacuum for the compressible euler equations with or without self gravitation first a general uniqueness theorem of classical solutions is proved for the three dimensional general motion second for the spherically symmetric motions without imposing the compatibility condition of the first derivative being zero at the center of symmetry a new local in time existence theory is established in a functional space involving less derivatives than those constructed for three dimensional motions in coutand et al commun math phys 296 559 587 2010 coutand and shkoller arch ration mech anal 206 515 616 2012 jang and masmoudi well posedness of compressible euler equations in a physical vacuum 2008 by constructing suitable weights and cutoff functions featuring the behavior of solutions near both the center of the symmetry and the moving vacuum boundary

half space problem for euler equations with damping in 3 d abstract in this paper we consider the half space problem for euler equations with damping in 3 d we restudy the fundamental solution for the cauchy problem to obtain an exponentially sharp pointwise structure and a clear decomposition of the singular regular components later both green s function for initial boundary value problem and fundamental solutions for cauchy problems are investigated in the transformed domain after laplace transform the symbols are obtained and a connection between green s function and fundamental solutions are established for the pointwise space time structure of green s function finally the sharp estimates for green s function together with a priori estimates from the energy method for high order derivatives result in the nonlinear stability of the solution and also the decaying rates

solutions of euler poisson equations for gaseous stars in this paper we study the euler poisson equations governing gas motion under self gravitational force we are interested in the evolution of the gaseous stars for which the density function has compact support we establish existence theory for the stationary solutions and describe the behavior of the solutions near the vacuum boundary the boundary behavior thus obtained agrees with the physical boundary condition proposed and studied in l ly for both euler equations with damping and the euler poisson equations existence non existence uniqueness and instability of the stationary solutions with vacuum are also discussed in terms of the adiabatic exponent and the entropy function and the phenomena of the blowup that is the collapsing of the star to a single point with finite mass as well as the drifting of part of the star to infinity in space are also studied and shown to agree with the conjecture from the physical considerations

global existence of smooth solutions and convergence to barenblatt solutions for the physical vacuum free boundary problem of compressible euler equations with damping for the physical vacuum free boundary problem with the sound speed being c1 2 holder continuous near vacuum boundaries of the one dimensional compressible euler equations with damping the global existence of the smooth solution is proved which is shown to converge to the barenblatt self similar solution for the porous media equation with the same total mass when the initial datum is a small perturbation of the barenblatt solution the pointwise convergence with a rate of density the convergence rate of velocity in the supremum norm and the precise expanding rate of the physical vacuum boundaries are also given the proof is based on a construction of higher order weighted functionals with both space and time weights capturing the behavior of solutions both near vacuum states and in large time an introduction of a new ansatz higher order nonlinear energy estimates and elliptic estimates 2016 wiley periodicals inc

gorenstein derived categories abstract gorenstein derived categories are defined and the relation with the usual derived categories is given the bounded gorenstein derived categories of gorenstein rings and of finite dimensional algebras are explicitly described via the homotopy categories of gorenstein projective modules and some applications are obtained gorenstein derived equivalences between cm finite gorenstein algebras are discussed

convergence to the barenblatt solution for the compressible euler equations with damping and vacuum we study the asymptotic behavior of a compressible isentropic flow through a porous medium when the initial mass is finite the model system is the compressible euler equation with frictional damping as t the density is conjectured to obey the well known porous medium equation and the momentum is expected to be formulated by darcy s law in this paper we give a definite answer to this conjecture without any assumption on smallness or regularity for the initial data we prove that any l weak entropy solution to the cauchy problem of damped euler equations with finite initial mass converges strongly in lp with decay rates to matching barenblatt s profile of the porous medium equation the density function tends to the barenblatt s solution of the porous medium equation while the momentum is described by darcy s law

asymptotic behavior of the solutions to the damped compressible euler equations with vacuum abstract the asymptotic behavior of solutions of the damped compressible euler equations is conjectured to obey to the famous porous media equations pmes the previous works on this topic concern the case away from vacuum where the system is strictly hyperbolic in present paper we prove that the l entropy weak solution with vacuum obtained by the compensated compactness theory converges strongly in l loc p 1 p space to the unique similarity solution of the related pme as time goes to infinity

expanding large global solutions of the equations of compressible fluid mechanics without any symmetry assumptions on the initial data we construct global in time unique solutions to the vacuum free boundary three dimensional isentropic compressible euler equations when the adiabatic exponent gamma lies in the interval 1 frac 5 3 our initial data lie sufficiently close to the expanding compactly supported affine motions recently constructed by sideris and they satisfy the physical vacuum boundary condition

formation of singularities in three dimensional compressible fluids presented are several results on the formation of singularities in solutions to the three dimensional euler equations for a polytropic ideal fluid under various assumptions on the initial data in particular it is shown that a localized fluid which is initially compressed and outgoing on average will develop singularities regardless of the size of the initial disturbance

convergence rate for compressible euler equations with damping and vacuum we study the asymptotic behavior of l weak entropy solutions to the compressible euler equations with damping and vacuum previous works on this topic are mainly concerned with the case away from the vacuum and small initial data in the present paper we prove that the entropy weak solution strongly converges to the similarity solution of the porous media equations in lp r 2 p with decay rates the initial data can contain vacuum and can be arbitrary large a new approach is introduced to control the singularity near vacuum for the desired estimates

the distributivity condition for uninorms and t operators in this work we study the functional equation given by the distributivity condition f x g y z g f x y f x z for all x y z 0 1 where the unknown functions f g are uninorms and or t operators we characterize all the solutions in the four possible cases i when f g are t operators ii when f is a t operator and g a uninorm iii when f is a uninorm and g a t operator and finally iv when f g are uninorms

compressible euler equations with vacuum abstract in this paper we first show that the regular solutions of compressible euler equations in r 3 with damping will not be global if the initial density function has compact support this implies that c 2 cannot be smooth across the boundary separating the gas and the vacuum after a finite time where c is the speed of sound then we study the local existence of solutions for isentropic gas flow in r when c 0 1 is smooth across using the energy method and the characteristics method

blowup of smooth solutions to the compressible navier stokes equation with compact density we present a sufficient condition on the blowup of smooth solutions to the compressible navier stokes equations in arbitrary space dimensions with initial density of compact support as an immediate application it is shown that any smooth solutions to the compressible navier stokes equations for polytropic fluids in the absence of heat conduction will blow up in finite time as long as the initial densities have compact support and an upper bound which depends only on the initial data on the blowup time follows from our elementary analysis immediately another implication is that there is no global small decay in time or even bounded in the case that all the viscosity coefficients are positive smooth solutions to the compressible navier stokes equations for polytropic fluids no matter how small the initial data are as long as the initial density is of compact support this is in contrast to the classical theory of global existence of small solutions to the same system with initial data being a small perturbation of a constant state that is not a vacuum the blowup of smooth solutions to the compressible euler system with initial density and velocity of compact support is a simple consequence of our argument 1998 john wiley sons inc

on some solutions of the distributivity equation abstract the aim of this paper is to present some interesting results on the distributivity equation for which several pairs of binary operations on 0 1 are considered moreover different methods to solve distributivity equations are used in this work

on the relation between k flatness and k projectivity abstract krause 19 has proved that the homotopy category k r pureproj of pure projective modules over an associative ring r is compactly generated and equivalent to the verdier quotient k r t r where t r is the triangulated subcategory of the homotopy category k r consisting of the pure acyclic complexes we provide an alternative proof of this result when restricted to the homotopy category of projective modules this equivalence reduces to that obtained by neeman 26 as an application of this description of k r pureproj we show that the k flat complexes defined by spaltenstein 29 are up to homotopy equivalence the filtered colimits of k projective complexes of pure projective modules

subdistributivity and superdistributivity of binary operations recently the property of distributivity of binary operations on 0 1 is of great interest both for practical as well as fundamental reasons in this paper we summarize some facts connected with distributivity and non distributivity of binary operations on 0 1 motivated by non distributive logical connectives in fuzzy set theory we show some new results concerning the above property a new direction of investigations mainly concerns the distributivity inequalities for triangular norms and conorms and their diverse generalizations in particular we look for examples of binary operations fulfilling the distributivity inequalities

waiting time for a non newtonian polytropic filtration equation with convection abstract in this paper we study the waiting time phenomena for a class of non newtonian polytropic filtration equation with convection according to the nonlinearity in the diffusion and the convection terms some necessary and sufficient conditions on the initial data are given for the existence of waiting time

some adjoints in homotopy categories let r be a ring in a previous paper 11 we found a new description for the category k r proj it is equivalent to the verdier quotient k r flat s for some suitable s c k r flat in this article we show that the quotient map from k r flat to k r flat s always has a right adjoint this gives a new fully faithful embedding of k r proj into k r flat its virtue is that it generalizes to nonaffine schemes

approximations and adjoints in homotopy categories we provide a criterion for the existence of right approximations in cocomplete additive categories it is a straightforward generalisation of a result due to el bashir this criterion is used to construct adjoint functors in homotopy categories applications include the study of pure derived categories for instance it is shown that the pure derived category of any module category is compactly generated

on the distributivity property for uninorms abstract distributivity between two operations is a property that was already posed many years ago and that is especially interesting in the framework of logical connectives for this reason the distributivity property has been extensively studied for several families of operations like triangular norms and conorms some kinds of uninorms and nullnorms also called t operators and even for some generalizations of them in this paper we investigate the distributivity equation involving two uninorms lying in any one of the most studied classes of uninorms leading to many new solutions

basic concepts for a theory of evaluation the aggregative operator abstract starting with an explication of the aggregative concept and deducing a general structure which satisfies a number of minimal requirements properties of clustering the main features of a new mathematical theory called theory of evaluation are developed the theory sheds new light on such well known concepts as membership conjunction and disjunction and seems to be a very promising tool to handle representation problems as they grow from the fields of theory of fuzzy set and its many applications of human decision making and of multicriteria analysis

structure of n uninorms in this paper we study binary operators on 0 1 which are associative monotone non decreasing in both variables and commutative amc with neutral element in this work we generalize the concept of neutral element and this generalization gives rise to a new class of amc binary operators on 0 1 called n uninorms n uninorms are denoted as u n where n comes from the generalization of the neutral element we study the structure of n uninorms the structure resembles an ordinal sum structure made up of n uninorms we characterize some special cases of them based on some continuity considerations and show that t norms t conorms uninorms and nullnorms t operators are special cases of n uninorms we also show that given n there are n 1 classes of operators in u n and each of them has many subclasses we also study the frank equation involving n uninorms and show that we need to consider only n uninorms for the study finally we show that the total number of subclasses of operators in u n follows the famous series called catalan numbers

the modularity law in some classes of aggregation operators abstract in this study we consider the functional equation of modularity in a special class of aggregation operators with an absorbing element first we focus on the modularity between commutative binary operators and their duals and then we examine the modularity for operators from the class of 2 uninorms which generalize nullnorms by extending their certain conditions in particular for these operators depending on the positions of their neutral elements and possessing the same absorbing element we obtain positive and negative results which are analogous to the results in the general case for operators with different absorbing elements

blowup of the solutions for the ibvp of the isentropic euler equations with damping abstract we establish several results about the blowup of the solutions for the initial boundary value problem of the isentropic euler equations with damping for a gas outside a ball under some assumptions on weighed functionals associated with the initial momentum that they are large enough to develop singularities

existence and asymptotic behavior of c1 solutions to the multi dimensional compressible euler equations with damping abstract in this paper the existence and asymptotic behavior of c 1 solutions to the multi dimensional compressible euler equations with damping on the framework of besov space are considered comparing with the well posedness results of sideris thomases wang t sideris b thomases d h wang long time behavior of solutions to the three dimensional compressible euler with damping comm partial differential equations 28 2003 953 978 we weaken the regularity assumptions on the initial data the global existence lies on a crucial a priori estimate which is obtained by the spectral localization method the main analytic tools are the littlewood paley decomposition and bony s paraproduct formula

half space problem of the system of compressible adiabatic flow through porous media in multi d abstract in this paper we consider the half space problem for the system of compressible adiabatic flow through porous media in 2 d and 3 d combining energy method green s function method and bootstrap method one establishes the decaying energy estimates which lead to global existence and optimal l 2 decaying rate of the solution finally for more large time information especially in spatial variables one applies green s function solution representation obtained by duhamel s principle and a priori estimate from energy method to obtain the space time pointwise structure of the solution

on gorenstein projective injective and flat dimensions a functorial description with applications gorenstein homological dimensions are refinements of the classical homological dimensions and finiteness singles out modules with amenable properties reflecting those of modules over gorenstein rings as opposed to their classical counterparts these dimensions do not immediately come with practical and robust criteria for finiteness not even over commutative noetherian local rings in this paper we enlarge the class of rings known to admit good criteria for finiteness of gorenstein dimensions

the homotopy category of flat modules and grothendieck duality let r be a ring we prove that the homotopy category k r proj is always aleph 1 compactly generated and depending on the ring r it may or may not be compactly generated we use this to give a description of k r proj as a quotient of k r flat the remarkable fact is that this new description of k r proj generalizes to non affine schemes this will appear in murfet s thesis

a priori estimates of local solutions to compressible navier stokes equations with free boundary abstract in this paper we consider the vacuum free boundary problem of the compressible navier stokes system in two dimension under the lagrangian variables we present a priori estimates of local in time solutions in a proper sobolev space

uninorms in fuzzy systems modeling abstract fuzzy systems modeling provides a framework in which input output relationships can be modeled by partitioning the input into fuzzy regions for which we can describe the output the fuzzy modeling inference process the procedure used to obtain the output of a fuzzy systems model for a given input is shown to involve an aggregation step in which the contributions of the different components of the fuzzy systems model are combined it is shown that the uninorm operator provides a general class of operators to implement this step the uninorm it is recalled is an operator that provides a generalization of the t norm and t conorm by allowing the identity element to be any value in the unit interval another step in the inference process is the determination of the contribution of each component of the model based on its relevancy to the current input the performance of this step requires the use of an operator related to the implication operator which we call a relevancy transformation ret operator it is shown that the form of this ret operator is dependent upon the identity value of the uninorm used in the aggregation step we provide some general formulations for this class of operators we show how the well known forms of fuzzy inference are special cases of our uninorm based approach

distributivity between uninorms and nullnorms recently the distributivity equation was investigated in families of certain operations e g triangular norms conorms uninorms and nullnorms generally the assumption of associativity is not necessary in consideration of distributivity equation moreover if we omit commutativity assumption consideration of the left and right distributivity conditions is reasonable previous results about distributivity between uninorms and nullnorms can be obtained as simple corollaries

local existence with physical vacuum boundary condition to euler equations with damping abstract in this paper we consider the local existence of solutions to euler equations with linear damping under the assumption of physical vacuum boundary condition by using the transformation introduced in lin and yang methods appl anal 7 3 2000 495 to capture the singularity of the boundary we prove a local existence theorem on a perturbation of a planar wave solution by using littlewood paley theory and justifies the transformation introduced in liu and yang 2000 in a rigorous setting

distributivity between semi t operators and semi nullnorms recently the distributivity equation was discussed in families of certain operations e g triangular norms conorms uninorms and nullnorms in this paper we describe the solutions of distributivity between semi t operators and semi nullnorms previous results about distributivity between nullnorms can be obtained as simple corollaries