the riemann problem for a class of nonlinear degenerate equations in the present paper we study the riemann problem for degenerate equations in which the pressure is constant over some range of stains by the liu entropy condition the riemann solutions of twelve regions in the v u plane are completely constructed moreover we obtain the invariant regions for the riemann solutions c 2012 elsevier inc all rights reserved

ladders and simplicity of derived module categories abstract recollements of derived module categories are investigated using a new technique ladders of recollements which are maximal mutation sequences the position in the ladder is shown to control whether a recollement restricts from unbounded to another level of derived category ladders also turn out to control derived simplicity on all levels an algebra is derived simple if its derived category cannot be deconstructed that is if it is not the middle term of a non trivial recollement whose outer terms are again derived categories of algebras derived simplicity on each level is characterised in terms of heights of ladders these results are complemented by providing new classes of examples of derived simple rings in particular indecomposable commutative rings as well as by a finite dimensional counterexample to the jordan holder problem for derived module categories moreover recollements are used to compute homological and k theoretic invariants

existence and uniqueness of multi bump bound states of nonlinear schrodinger equations with electromagnetic fields abstract in this paper we are concerned with the existence and uniqueness of multi bump bound states of the nonlinear schrodinger equations with electromagnetic potential i t i a x 2 v x p 2 x r n for sufficiently small 0 where i is the imaginary unit 2 p 2 n n 2 for n 3 and 2 p for n 1 2 v x is a bounded real function on r n and a x a 1 x a 2 x a n x is such that a j x is a bounded real function on r n for j 1 2 n for any finite collection of a 1 a 2 a k of non degenerate critical points of v x we show that there exists a solution x t exp iet u x which is a small perturbation of a sum of one bump solutions concentrated at a 1 a 2 a k and u x is unique up to rotations for small 0

travelling wave solutions for a balance law we study entropy travelling wave solutions for first order hyperbolic balance laws results concerning existence regularity and asymptotic stability of such solutions are proved for convex fluxes and source terms with simple isolated zeros

simplicial structures in higher auslander reiten theory abstract we develop a novel combinatorial perspective on the higher auslander algebras of type a a family of algebras arising in the context of iyama s higher auslander reiten theory this approach reveals interesting simplicial structures hidden within the representation theory of these algebras and establishes direct connections to eilenberg maclane spaces and higher dimensional versions of waldhausen s s construction in algebraic k theory as an application of our techniques we provide a generalisation of the higher reflection functors of iyama and oppermann to representations with values in stable categories the resulting combinatorial framework of slice mutation can be regarded as a higher dimensional variant of the abstract representation theory of type a quivers developed by groth and s ovicek our simplicial point of view then naturally leads to an interplay between slice mutation horn filling conditions and the higher segal conditions of dyckerhoff and kapranov in this context we provide a classification of higher segal objects with values in any abelian category or stable category

existence and asymptotic behavior of solutions to inhomogeneous equations of elasticity with little viscosity we study the existence and asymptotic behavior of the solutions to inhomogeneous equations of elasticity with little viscosity u t x v f u v eu xx v t u x g u v ev xx with initial value u v x 0 u 0 x v 0 x here v is a given smooth strongly monotone function on r v a 2 v a v 0 ver and f u v and g u v are given smooth functions on r 2 and e is a positive constant

multi bump bound states for a system of nonlinear schrodinger equations abstract motivated by problems arising in nonlinear optics and bose einstein condensates we consider in r n with n 3 the following system of coupled schrodinger equations u i v i x u i u i j 1 d i j u j 2 u i 0 lim x u i x 0 i 1 d where 0 is a parameter i j j i are positive constants and v i non negative given potentials we assume that the interior of i 1 d v i 1 0 admits m connected components 1 m which are of class c 1 and isolated in each v i 1 0 for each non empty j 1 m we prove that the system admits for any large a multi bump solution u r n r d which is small in r n j j j and on each j j j close in h 1 norm to a least energy solution of the limit problem u i u i j 1 d i j u j 2 i 1 d subjected to homogeneous dirichlet boundary condition an explicit condition on the matrix i j is given to ensure our solutions have at least two positive components

quasiconvexity and relaxation of nonconvex problems in the calculus of variations keywords quasiconvexity relaxation reference caa article 1982 002doi 10 1016 0022 1236 82 90046 5view record in web of science record created on 2008 11 25 modified on 2017 05 12

nonlinear stability of rarefaction waves for compressible navier stokes equations it is shown that expansion waves for the compressible navier stokes equations are nonlinearly stable the expansion waves are constructed for the compressible euler equations based on the inviscid burgers equation our result shows that navier stokes equations and euler equations are time asymptotically equivalent on the level of expansion waves the result is proved using the energy method making essential use of the expansion of the underlining nonlinear waves and the specific form of the constitutive eqution for a polytropic gas

convergence of the viscosity method for isentropic gas dynamics a convergence theorem for the method of artificial viscosity applied to the isentropic equations of gas dynamics is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

the role of the green s function in a non linear elliptic equation involving the critical sobolev exponent this paper is concerned with non linear elliptic problems of the type pe u u n 2 n 2 eu u 0 on u 0 on where is a smooth and bounded domain in rn n 4 and e 0 we show that if the ue are solutions of pe which concentrate around a point as e 0 then this point cannot be on the boundary of and is a critical point of the regular part of the green s function conversely we show that for n 5 and any non degenerate critical point x0 of the regular part of the green s function there exist solutions of pe concentrating around x0 as e 0

solutions with multiple peaks for nonlinear elliptic equations solutions with peaks near the critical points of q x are constructed for the problem delta u lambda 2 u q x u p 2 u x is an element of r n u is an element of h 1 and 2 p 2n n 2

asymptotic stability of rarefaction waves for 2 2 viscous hyperbolic conservation laws the two modes case abstract in this paper we continue our study on the asymptotic behavior toward rare faction waves of a general 2 2 system of hyperbolic conservation laws with positive viscosity matrix it is shown that when the initial data is a small perturbation of a weak rarefaction wave a linear superposition of a 1 rarefaction wave and a 2 rarefaction wave for the corresponding inviscid hyperbolic conservation laws then the solution of the cauchy problem for the viscous system globally exists and tends to the rarefaction wave the result is proved by using an energy method combining the technique in z p xin j differential equations 73 1988 45 77 and using the characteristic energy method of t p liu mem amer math soc 328 1975 1 108

uniqueness of positive multi lump bound states of nonlinear schrodinger equations in this paper we are concerned with multi lump bound states of the nonlinear schrodinger equation

higher nakayama algebras i construction we introduce higher dimensional analogues of the nakayama algebras from the viewpoint of iyama s higher auslander reiten theory more precisely for each nakayama algebra a and each positive intege

abstract representation theory of dynkin quivers of type a abstract we study the representation theory of dynkin quivers of type a in abstract stable homotopy theories including those associated to fields rings schemes differential graded algebras and ring spectra reflection functors partial coxeter functors and serre functors are defined in this generality and these equivalences are shown to be induced by universal tilting modules certain explicitly constructed spectral bimodules in fact these universal tilting modules are spectral refinements of classical tilting complexes as a consequence we obtain split epimorphisms from the spectral picard groupoid to derived picard groupoids over arbitrary fields these results are consequences of a more general calculus of spectral bimodules and admissible morphisms of stable derivators as further applications of this calculus we obtain examples of universal tilting modules which are new even in the context of representations over a field this includes yoneda bimodules on mesh categories which encode all the other universal tilting modules and which lead to a spectral serre duality result finally using abstract representation theory of linearly oriented a n quivers we construct canonical higher triangulations in stable derivators and hence a posteriori in stable model categories and stable categories

global stability of viscous contact wave for 1 d compressible navier stokes equations the viscous contact waves for one dimensional compressible navier stokes equations has recently been shown to be asymptotically stable the stability results are called local stability or global stability depending on whether the norms of initial perturbations are small or not up to now local stability results toward viscous contact waves of compressible navier stokes equations have been well established see huang et al 2006 2008 2009 9 10 7 but there are few results for the global stability in the case of cauchy problem which is the purpose of this paper the proof is based on an elementary energy method using an inequality concerning the heat kernel see lemma 1 of huang et al 2010 7

decay rates of solutions to the cauchy problem for dissipative nonlinear evolution equations abstract in this paper we study the global existence and the asymptotic behavior of the solutions to the cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects e t 1 x x x t 1 x x x x with initial data i x 0 0 x 0 x as x where and are positive constants such that 1 1 through constructing a correct function x t defined by 2 13 and using the energy method we show sup x r x t x x x t 0 as t and the solutions decay with exponential rates the same problem was studied by tang and zhao s q tang h j zhao nonlinear stability for dissipative nonlinear evolution equations with ellipticity j math anal appl 233 1999 336 358 for the case of 0 0

large time behaviors of solutions to an inflow problem in the half space for a one dimensional system of compressible viscous gas the inflow problem for a one dimensional compressible barotropic flow on the half line r 0 is investigated not only classical waves but also the new wave which is called the boundary layer solution arise large time behaviors of the solutions to be expected have been classified in terms of the boundary values by a matsumura inflow and outflow problems in the half space for a one dimensional isentropic model system of compressible viscous gas to appear in proceedings of ims conference on differential equations from mechanics hong kong 1999 in this paper we give the rigorous proofs of the stability theorems on both the boundary layer solution and a superposition of the boundary layer solution and the rarefaction wave

nonlinear stability of strong rarefaction waves for the generalized kdv burgers kuramoto equation with large initial perturbation abstract in was shown in ruan et al 2008 3 that rarefaction waves for the generalized kdv burgers kuramoto equation are nonlinearly stable provided that both the strength of the rarefaction waves and the initial perturbation are sufficiently small the main purpose of this work is concerned with nonlinear stability of strong rarefaction waves for the generalized kdv burgers kuramoto equation with large initial perturbation in our results we do not require the strength of the rarefaction waves to be small and when the smooth nonlinear flux function satisfies certain growth condition at infinity the initial perturbation can be chosen arbitrarily in h 1 r while for a general smooth nonlinear flux function we need to ask for the l 2 norm of the initial perturbation to be small but the l 2 norm of the first derivative of the initial perturbation can be large and consequently the h 1 r norm of the initial perturbation can also be large

n representation infinite algebras abstract from the viewpoint of higher dimensional auslander reiten theory we introduce a new class of finite dimensional algebras of global dimension n which we call n representation infinite they are a certain analog of representation infinite hereditary algebras and we study three important classes of modules n preprojective n preinjective and n regular modules we observe that their homological behaviour is quite interesting for instance they provide first examples of algebras having infinite ext 1 orthogonal families of modules moreover we give general constructions of n representation infinite algebras applying minamoto s theory on fano algebras in non commutative algebraic geometry we describe the category of n regular modules in terms of the corresponding preprojective algebra then we introduce n representation tame algebras and show that the category of n regular modules decomposes into the categories of finite dimensional modules over localizations of the preprojective algebra this generalizes the classical description of regular modules over tame hereditary algebras as an application we show that the representation dimension of an n representation tame algebra is at least n 2

asymptotic stability of traveling wave solutions of systems for one dimensional gas motion the asymptotic stability of traveling wave solutions with shock profile is investigated for several systems in gas dynamics 1 the solution of a scalar conservation law with viscosity approaches the traveling wave solution at the ratet for some 0 ast provided that the initial disturbance is small and of integral zero and in addition decays at an algebraic rate for x 2 the traveling wave solution with nishida and smoller s condition of the system of a viscous heat conductive ideal gas is asymptotically stable provided the initial disturbance is small and of integral zero 3 the traveling wave solution with weak shock profile of the broadwell model system of the boltzmann equation is asymptotically stable provided the initial disturbance is small and its hydrodynamical moments are of integral zero each proof is given by applying an elementary energy method to the integrated system of the conservation form of the original one the property of integral zero of the initial disturbance plays a crucial role in this procedure

asymptotic stability of rarefaction waves for 2 2 viscous hyperbolic conservation laws this paper concerns the asymptotic behavior toward rarefaction waves of the solution of a genera 2 x 2 hyperbolic conservation laws with positive viscosity we prove that if the initial data is close to a constant state and its values at a3 lie on the kth rarefaction curve for the corresponding hyperbolic conservation laws then the solution tends as i co to the rarefaction wave determined by these states

the cyclic homology of crossed product algebras in their article 9 on cyclic homology feigin and tsygan have given a spectral sequence for the cyclic homology of a crossed product algebra generalizing burghelea s calculation 4 of the cyclic homology of a group algebra for an analogous spectral sequence for the hochschild homology of a crossed product algebra see brylinski 2 3 in this article we give a new derivation of this spectral sequence and generalize it to negative and periodic cyclic homology hc a and hp a the method of proof is itself of interest since it involves a natural generalization of the notion of a cyclic module in which the condition that the morphism n n is cyclic of order n 1 is relaxed to the condition that it be invertible we call this category the paracyclic category given a paracyclic module p we can define a chain complex c p with differentials b and b which respectively lower and raise degree the condition that the module p is paracyclic translates to the condition on c p that 1 bb bb is invertible our main result is to show that there is an analogue of the eilenberg zilber theorem for bi paracyclic modules it is then easy to obtain a new expression for the cyclic homology of a crossed product algebra which leads immediately to the spectral sequence of feigin and tsygan if m is a module over a commutative ring k we will denote by m k the iterated tensor product defined by m 0 k and m k 1 m k m if m and n are graded modules we will denote by m n their graded tensor product we would like to thank j block j l brylinski and c kassel for a number of interesting discussions on the results presented here

positively invariant regions for a problem in phase transitions positively invariant regions for the system v t p w x e v xx w t v x e w x are constructed where p p w 0 w e 0 such a choice of p is motivated by the maxwell construction for a van der waals fluid the method of an analysis is a modification of earlier ideas of chueh conley smoller 1 the results given here provide e independent l bounds on the solution w v

adaptive finite element methods for conservation laws based on a posteriori error estimates we prove a posteriori error estimates for a finite element method for systems of strictly hyperbolic conservation laws in one space dimension and design corresponding adaptive methods the proof of the a posteriori error estimates is based on a strong stability estimate for an associated dual problem together with the galerkin orthogonality of the finite element method the strong stability estimate uses the entropy condition for the system in an essential way 1995 john wiley sons inc

a model for the homotopy theory of homotopy theory we describe a category the objects of which may be viewed as models for homotopy theories we show that for such models functors between two homotopy theories form a homotopy theory or more precisely that the category of such models has a well behaved internal hom object

group cohomology and the cyclic cohomology of crossed products definite results are obtained in the conditions the group g is torsion free and the class h of the extension 0 zh g h n h 0 in h2 nh k is niipotent here gh for h g stands for the centralizer of h the cyclic homology groups hc a g decompose naturally as a direct sum of two subgroups called the homogeneous and the inhomogeneous parts ofhc a g the homogeneous part can be obtained from a spectral sequence converging to it with e2 q hp g hcq a the inhomogeneous part vanishes after inverting s for g z and in the topological situation we thus reobtain the result of nest 17 for general g but a k and trivial action thus for group rings k g we reobtain results of burghelea 4 the free groups satisfy our conditions see 10 for other classes of groups satisfying these conditions in this case our results are compatible with the results of pimsner and voiculescu 18 19 and suggest that for a large class of groups the part of ktor a r d g is obtained from a convergent spectral sequence with e q hp g k here r176 denotes the topological k theory functors see 2 a is a c algebra and a d g the reduced crossed product c algebra is a suitable completion of a g kasparov 13 succeeded to prove this for groups having a special manifold as classifying space we expect that our spectral sequence will give more insight in kasparov s spectral sequence we also mention

higher dimensional auslander reiten theory on maximal orthogonal subcategories abstract we introduce the concept of maximal n 1 orthogonal subcategories over artin algebras and orders and develop n 1 dimensional auslander reiten theory on them we give the n auslander reiten translation and the n auslander reiten duality then show the existence of n almost split sequences and n fundamental sequences we give some examples

asymptotic stability of planar rarefaction waves for viscous conservation laws in several dimensions this paper concerns the large time behavior toward planar rarefaction waves of the solutions for scalar viscous conservation laws in several dimensions it is shown that a planar rarefaction wave is nonlinearly stable in the sense that it is an asymptotic attractor for the viscous conservation law this is proved by using a stability result of rarefaction wave for scalar viscous conservation laws in one dimension and an elementary l 2 energy method 0 introduction we will establish the asymptotic stability of planar rarefaction waves for scalar viscous conservation laws in two or more space dimensions we consider n dimensional scalar viscous conservation laws of the form n n 1 ut el f u x e aijux1u x e r t 0 i 1 i j l where u e r1 a aij called the viscosity matrix is a constant positive definite matrix and we assume that all the flux functions are smooth say in cn and equation 1 is genuinely nonlinear in the x1 direction 8 i e for a fixed constant a 0 2 jf u a the initial data for equation 1 is 3 u x o uo x satisfying 4 lim u x1 u ilx rn i 0 where u u u are two constants a planar rarefaction wave in x1 direction ur xl t is a solution of the following initial value problem for the received by the editors september 27 1988 1980 mathematics subject classification 1985 revision primary 35q99 35k35

multi bump solutions for the nonlinear schrodinger poisson system in this paper we study a kind of nonlinear schrodinger poisson system with a parameter e for any positive integer m we prove that there exists e m 0 such that for 0 e e m the equation has an m bump positive solution under some suitable conditions as a consequence the equation has more and more multi bump positive solutions as e 0

viscous solutions of quadratic conservation laws with umbilic points viscous solutions of quadratic conservation laws with umbilic points ltj yunguang zhu changjiang and zhao huijiang wuhan institute of mathematical sciences academia sinica wuhan 430071 people s republic of china received 10 january 1991 received in revised form 4 august 1992 received for publication 1 march 1993

n angulated categories we dene n angulated categories by modifying the axioms of triangulated categories in a natural way we show that heller s parametrization of pre triangulations extends to pre n angulations we obtain a large class of examples of n angulated cate gories by considering n 2 cluster tilting subcategories of triangulated categories which are stable under the n 2 nd power of the suspension functor as an application we show how n angulated calabi yau categories yield triangulated calabi yau categories of higher calabi yau dimension finally we sketch a link to algebraic geometry and string theory

n representation finite algebras and n apr tilting we introduce the notion of n representation finiteness generalizing representationfinite hereditary algebras we establish the procedure of n apr tilting and show that it preserves n representation finiteness we give some combinatorial description of this procedure and use this to completely describe a class of n representation finite algebras called type a

a case study of global stability of strong rarefaction waves for 2 2 hyperbolic conservation laws with artificial viscosity this paper is concerned with the global stability of strong rarefaction waves for a class of 2 x 2 hyperbolic conservation laws with artificial viscosity i e the p system with artificial viscosity

tilting theory via stable homotopy theory we show that certain tilting results for quivers are formal consequences of stability and as such are part of a formal calculus available in any abstract stable homotopy theory thus these results are for example valid over arbitrary ground rings for quasi coherent modules on schemes in the differential graded context in stable homotopy theory and also in the equivariant motivic or parametrized variant thereof in further work we will continue developing this calculus and obtain additional abstract tilting results here we also deduce an additional characterization of stability based on goodwillie s strongly co cartesian n cubes as applications we construct abstract auslander reiten translations and abstract serre functors for the trivalent source and verify the relative fractionally calabi yau property this is used to offer a new perspective on may s axioms for monoidal triangulated categories