proof of existence of global solutions for m component reaction diffusion systems with mixed boundary conditions via the lyapunov functional method to prove global existence for solutions of m component reaction diffusion systems presents fundamental difficulties in the case in which some components of the system satisfy neumann boundary conditions while others satisfy nonhomogeneous dirichlet boundary conditions and nonhomogeneous robin boundary conditions the purpose of this paper is to prove the existence of a global solution using a single inequality for the polynomial growth condition of the reaction terms our technique is based on the construction of polynomial functionals this result generalizes those obtained recently by kouachi et al at press kouachi 2002 electron j diff eqns 2002 1 kouachi 2001 electron j diff eqns 2001 1 and independently by malham and xin 1998 commun math phys 193 287

perturbation bound of the drazin inverse a perturbation theory for the drazin inverse a d is developed this theory is based on the jordan canonical form of a norm estimates of a e a d are derived when a d and a e are of the same rank and e is small a hard problem by campbell and meyer linear algebra appl 10 1975 77 83 is partially solved

global existence for reaction diffusion systems with mass control and critical growth with respect to the gradient abstract in this paper we study the existence of global weak solutions for 2 2 reaction diffusion systems for which two main properties hold the positivity of the solutions and the total mass of the components are preserved with time moreover we suppose that the non linearities have critical growth with respect to the gradient the technique we use here in order to prove global existence is in the same spirit of the method developed by boccardo murat and puel for a single equation

a sufficient condition for blowup solutions of nonlinear heat equations abstract the author discusses the initial boundary value problem ui t ui fi u1 um with u i 0 and ui x 0 i x i 1 m in a bounded domain r n under suitable assumptions on fi he proves that if i 1 e0 i in d i for some small e0 0 then the solutions blow up in a finite time where i is a positive solution of i fi 1 m 0 with i di 0 for i 1 m if m 1 the initial value can be negative in a subset of

perturbation of the drazin inverse for matrices with equal eigenprojections at zero abstract let a denote the eigenprojection of a matrix a corresponding to the eigenvalue 0 we characterize matrices b such that b a and derive from the results 1 error bounds for the drazin inverse of a perturbation 2 improvement of error bounds given recently by wei 10 wei and wang 11 and castro gonzalez et al 4 and 3 a new characterization of ep matrices

symmetrically separated sequences in the unit sphere of a banach space abstract we prove the symmetric version of kottman s theorem that is to say we demonstrate that the unit sphere of an infinite dimensional banach space contains an infinite subset a with the property that x y 1 for distinct elements x y a thereby answering a question of j m f castillo in the case where x contains an infinite dimensional separable dual space or an unconditional basic sequence the set a may be chosen in a way that x y 1 e for some e 0 and distinct x y a under additional structural properties of x such as non trivial cotype we obtain quantitative estimates for the said e certain renorming results are also presented

the perturbation theory for the drazin inverse and its applications abstract let a and e be n n matrices and b a e denote the drazin inverse of a by ad we give an upper bound for the relative error b d a d a d under certain circumstances an error bound for the solution for the singular equations ax b b r a is also considered

influence of mixed boundary conditions in some reaction diffusion systems we analyse global existence of solutions to a system of two reaction diffusion equations for whicha balance law holds the main aim is to make clear the influence of different combinations ofboundary conditions on global existence under the assumption that the nonlinearities satisfy polynomial growth estimates

star finite coverings of banach spaces abstract we study star finite coverings of infinite dimensional normed spaces a family of sets is called star finite if each of its members intersects only finitely many other members of the family it follows from our results that an lur or a uniformly frechet smooth infinite dimensional banach space does not admit star finite coverings by closed balls on the other hand we present a quite involved construction of a star finite covering of c 0 by frechet smooth centrally symmetric bounded convex bodies a similar but simpler construction shows that every normed space of countable dimension and hence incomplete has a star finite covering by closed balls

multiplicity results for a neumann problem involving the p laplacian abstract in this paper we establish some multiplicity results for the following neumann problem div u p 2 u x u p 2 u x f u in u 0 on the multiple solutions are obtained by combining an existence theorem recently proved by g anello and g cordaro with well known critical point theorems

on the inverse mean first passage matrix problem and the inverse m matrix problem abstract the inverse mean first passage time problem is given a positive matrix m r n n then when does there exist an n state discrete time homogeneous ergodic markov chain c whose mean first passage matrix is m the inverse m matrix problem is given a nonnegative matrix a then when is a an inverse of an m matrix the main thrust of this paper is to show that the existence of a solution to one of the problems can be characterized by the existence of a solution to the other in so doing we extend earlier results of tetali and fiedler

existence of solutions for a class of weakly coupled semilinear elliptic systems on etudie l existence des solutions de problemes aux limites pour des systemes elliptiques semi lineaires

characterizations of inverse m matrices with special zero patterns in this paper we provide some characterizations of inverse m matrices with special zero patterns in particular we give necessary and sufficient conditions for k diagonal matrices and symmetric k diagonal matrices to be inverse m matrices in addition results for triadic matrices tridiagonal matrices and symmetric 5 diagonal matrices are presented as corollaries

perturbation bounds for the generalized inverses at s 2 with application to constrained linear system in this paper the more general perturbation problem of the generalized inverse a t s 2 is considered we derive its perturbation bounds when the subspaces t and s also have perturbation and in special case when t and s have no perturbation we get some results on the condition numbers with respect to a t s 2 and constrained linear system ax b x t which are similar to the regular inverse a 1 and nonsingular linear system ax b

global existence and convergence to a singular steady state for a semilinear heat equation with certain initial and boundary conditions the solution u to the semilinear heat equation u t u f u where f is a positive superlinear function and is the supremum of the open spectrum for the steady state problem w f w 0 is found to exist for all time and to be unbounded moreover u approaches w a singular steady state as tends to infinity

continuity properties of the 1 inverse and perturbation bounds for the drazin inverse there are known results about the continuity of the important pseudoinverses we extend some well known results to the 1 inverse as for the drazin inverse which is not a 1 inverse we present new perturbation bounds

multiple solutions for two nonlinear problems involving the p laplacian abstract using variational arguments we prove the existence of at least two solutions for two elliptic problems involving the p laplacian dirichlet and neumann boundary conditions will be considered in the two problems where a positive parameter appears

error bounds for a general perturbation of the drazin inverse the paper solves a long standing problem of finding error bounds for a general perturbation of the drazin inverse the bounds are given in terms of the distance between the matrices together with the distance between their eigenprojections estimates using the gap between subspaces are also given recent results of several authors including castro koliha straskraba soochov j math to appear wang and wei linear algebra appl 258 1997 179 186 can be recovered as special cases of our theorems

singularly perturbed boundary value problems in case of exchange of stabilities we consider a mixed boundary value problem for a system of two second order nonlinear differential equations where one equation is singularly perturbed we assume that the associated equation has two intersecting families of equilibria this property excludes the application of standard results by means of the method of upper and lower solutions we prove the existence of a solution of the boundary value problem and determine its asymptotic behavior with respect to the small parameter the results can be used to study differential systems modeling bimolecular reactions with fast reaction rates

qualitative theory for a model of laminar flames with arbitrary nonnegative initial data abstract we consider a system of nonlinear parabolic partial differential equations arising as a model of laminar flames in a premixed reactive gas the existence of traveling wave solutions has been established for positive ignition temperature by berestycki nicolaenko and scheurer and by terman for zero ignition temperature stability and instability of these solutions have been established in various situations by sivashinsky clavin and recently terman our goal is to study the equations with initial data that are bounded uniformly continuous and nonnegative but otherwise arbitrary we establish the existence of unique global strong solutions satisfying appropriate a priori estimates with a positivity condition imposed on the initial data for the temperature we show that the concentration decays exponentially this result while easy to obtain plays an important role in results that follow of greatest physical interest are the cases where ignition occurs precisely at one end our main result is that if the average of the initial temperature values at the ends of the chamber is above ignition temperature then on any ray coming from the ignition end the temperature is uniformly above ignition temperature and the concentration decays uniformly to zero we can continually advance the endpoint of this zone of ignition thus roughly mimicking the motion of traveling wave solutions we also point out the appropriateness of the averaging condition on the initial temperature and discuss two examples where this averaging condition is not satisfied in one we eventually have flame propagation and in the other example we have eventual flame extinguishment on any ray coming from the cold end of the chamber

the drazin inverse of a modified matrix we derive the expression for the drazin inverse of a modified matrix the perturbation bound for the drazin inverse is also established i e the open problem posed by campbell and meyer in 1975 has been partially solved

acute perturbation of the group inverse abstract for any n n complex matrix a let a g be the group inverse of a when a is singular a matrix b a e is said to be an acute perturbation of a if e is small and the spectral radius b g b a g a 1 the acute perturbation coincides with the stable perturbation of the group inverse if the matrix b satisfies condition r b n a 0 n b r a 0 which was introduced by castro gonzalez et al 2008 8 furthermore several examples are provided to illustrate the acute perturbation of the group inverse

on systems of reaction diffusion equations with a balance law the sequel abstract this paper is a sequel of the review paper on reaction diffusion systems with a balance law by martin and pierre 1990 here we present the results obtained after martin and pierre 1990 not only for classical systems but also for systems with either time fractional derivatives or space fractional derivatives accounting for anomalous diffusions

error bounds for the perturbation of the drazin inverse under some geometrical conditions this paper studies the drazin inverse for perturbed matrices for that given a square matrix a we consider and characterize the class of matrices b with index s such that r ba d n a d 0 n a db r a d 0 and r b s r ba d where n a and r a denote the null space and the range space of a matrix a respectively and a d denote the drazin inverse of a then we provide explicit representations for b d and bb d and upper bounds for the relative error b d a email protected a email protected and the error bb d aa email protected a numerical example illustrates that the obtained bounds are better than others given in the literature

gδ embeddings in hilbert space abstract it is shown that a separable banach space x has the point of weak to norm continuity property resp the radon nikodym property if and only if there exists a compact g embedding resp an h embedding from x into l2 this solves several questions of j bourgain and h p rosenthal j funct anal 52 1983 it is also shown that every non relatively compact sequence in a banach space with property pc has a difference subsequence which is a boundedly complete basic sequence this solves a question of pelczynski and extends some results of w b johnson and h p rosenthal studia math 43 1972 77 92 various related questions asked in the above bourgain rosenthal reference and by g a edgar and r f wheeler pac j math 115 1984 and n ghoussoub and h p rosenthal math ann 264 1983 321 332 are also settled

boundedness and blow up for a semilinear reaction diffusion system abstract we consider the semilinear parabolic system s u t u p t u q where x rnn 1 t 0 and p q are positive real numbers at t 0 nonnegative continuous and bounded initial values u0 v0 x are prescribed the corresponding cauchy problem then has a nonnegative classical and bounded solution u t x v t x in some strip st 0 t r n 0 t sup t 0 u v remain bounded in s t we show in this paper that if 0 t so that solutions can be continued for all positive times when pq 1 and 1 pq 1 n 2 with max p q one has t for every nontrivial solution u v t is then called the blow up time of the solution under consideration finally if 1 pq 1 n 2 both situations coexist since some nontrivial solutions remain bounded in any strip s while others exhibit finite blow up times

the error bound of the perturbation of the drazin inverse abstract let a and e be n n matrices and b a e denote the drazin inverse of a by a d in this paper we give an upper bound for the relative error b d a d a d 2 and a lower bound for b d 2 under certain circumstances the continuity properties and the derivative of the drazin inverse are also considered

additive perturbation results for the drazin inverse abstract in this paper some new additive results for the drazin inverse are presented we give a formula for the drazin inverse of a sum of two matrices under conditions on the matrices less restrictive than those imposed in the corresponding theorem given by hartwig et al linear algebra appl 322 2001 207 217 we consider some aplications of our results to the perturbation of the drazin inverse and analyze a number of special cases

initial boundary value problem for a singularly perturbed parabolic equation in case of exchange of stability the theorem on passage to the limit is proved for a singularly perturbed parabolic problem in case when the degenerate equation has two intersecting roots

an expression of the drazin inverse of a perturbed matrix given a square matrix a and its perturbation matrix e a new expression for the drazin inverse b d of b a e is derived if aa db 2 aa db 2 or b 2aa d baa d 2 based on the new expression a bound of the relative error of b d is developed some known results in the literature on the drazin inverse and the perturbation bound are included by this new formula as special cases a numerical example is given to compare the upper bounds

global existence and asymptotic behavior for a time fractional reactiondiffusion system this paper is concerned with the existence of global in time solutions of a time fractional reactiondiffusion system with time fractional derivatives furthermore the large time behavior of bounded solutions is investigated our method of proof relies on a maximal regularity result for fractional linear reactiondiffusion equations that has been derived by bajlekova 2001

a note on the perturbation bound of the drazin inverse a perturbation bound for the drazin inverse a d with ind a e 1 has recently been developed however those upper bounds are not satisfied since it is not tight enough in this paper a sharper upper bounds for a e a d with weaker conditions is derived that new bound is also a generalization of a new general upper bound of the group inverse we also derive a new expression of the drazin inverse a e d with ind a e 1 and the corresponding upper bound of a e d a d in a special case numerical examples are given to illustrate the sharpness of the new bounds

existence of inertial manifolds for partly dissipative reaction diffusion systems in higher space dimensions abstract in this paper we prove the existence of inertial manifolds for a partly dissipative reaction diffusion system of the form formula where is a rectangular domain in r 2or a cubic domain in r 3 the proof is based on an abstract invariant manifold theorem for semiflows in a hilbert space which is proved by using the graph transform method the principle of spatial averaging also plays an important role in the proof

interior estimates for a class of reaction diffusion systems from l1 a priori estimates abstract we obtain interior estimates for a class of semilinear reaction diffusion systems from l 1 a priori estimates our results are applied to a predator prey model in which the species switch the role of predator and prey on given subsets of their domain of interaction and a one dimensional flame propagation model extensions of earlier results in morgan 14 15 follow from the analysis

reaction diffusion systems with initial data of low regularity abstract models issued from ecology chemical reactions and several other application fields lead to semi linear parabolic equations with super linear growth even if in general blow up can occur these models share the property that mass control is essential in many circumstances it is known that this l 1 control is enough to prove the global existence of weak solutions the theory is based on basic estimates initiated by m pierre and collaborators who have introduced methods to prove l 2 a priori estimates for the solution here we establish such a key estimate with initial data in l 1 while the usual theory uses l 2 this allows us to greatly simplify the proof of some results we also establish new existence results of semilinearity which are super quadratic as they occur in complex chemical reactions our method can be extended to semi linear porous medium equations

inertial manifolds associated to partly dissipative reaction diffusion systems abstract in a previous work we established the existence of finite dimensional attractors for partly dissipative reaction diffusion systems of two types systems with a polynomial growth nonlinearity and systems admitting an invariant region the aim of this article is to show that these problems possess inertial manifolds in space dimension n 2 these inertial manifolds contain the universal attractor attract exponentially all the solutions as time goes to infinity and due to the weak dissipation are here infinite dimensional our results are applied to several classical systems borrowed from mathematical biology physics and chemistry