identification of sparse linear operators we consider the problem of identifying a linear deterministic operator from its response to a given probing signal for a large class of linear operators we show that stable identifiability is possible if the total support area of the operator s spreading function satisfies 1 2 this result holds for an arbitrary possibly fragmented support region of the spreading function does not impose limitations on the total extent of the support region and most importantly does not require the support region to be known prior to identification furthermore we prove that stable identifiability of almost all operators is possible if 1 this result is surprising as it says that there is no penalty for not knowing the support region of the spreading function prior to identification algorithms that provably recover all operators with 1 2 and almost all operators with 1 are presented

chemotaxis with logistic source very weak global solutions and their boundedness properties abstract we consider the chemotaxis system u t u u v g u x t 0 0 v v u x t 0 in a smooth bounded domain r n where 0 and g generalizes the logistic function g u a u b u with 1 a 0 and b 0 a concept of very weak solutions is introduced and global existence of such solutions for any nonnegative initial data u 0 l 1 is proved under the assumption that 2 1 n moreover boundedness properties of the constructed solutions are studied inter alia it is shown that if b is sufficiently large and u 0 l has small norm in l for some n 2 then the solution is globally bounded finally in the case that additionally n 2 holds a bounded set in l can be found which eventually attracts very weak solutions emanating from arbitrary l 1 initial data the paper closes with numerical experiments that illustrate some of the theoretically established results

on the existence of weak solutions of nonlinear degenerate parabolic system with variable exponents abstract the main goal of the present paper is establishing the existence and uniqueness of weak solutions for the nonlinear degenerate reaction diffusion system with variable exponents a model also is proposed to characterize the invasion of cancer cells towards healthy cells with acidification environment moreover the main results of this paper are obtained using regularization problem the faedo galerkin approximation method some apriori estimates compactness results and the gronwall lemma

persistence in higher dimensions a finite size scaling study we show that the persistence probability p t l in a coarsening system of linear size l at a time t has the finite size scaling form p t l l zef jj where 9 is the persistence exponent and z is the coarsening exponent the scaling function f x x e for x 1 and is constant for large x the scaling form implies a fractal distribution of persistent sites with power law spatial correlations we study the scaling numerically for glauber ising model at dimension d 1 to 4 and extend the study to the diffusion problem our finite size scaling ansatz is satisfied in all these cases providing a good estimate of the exponent 9

bounds for blow up time in nonlinear parabolic problems abstract a first order differential inequality technique is used on suitably defined auxiliary functions to determine lower bounds for blow up time in initial boundary value problems for parabolic equations of the form u t div u grad u f u if blow up occurs in addition conditions which ensure that blow up occurs or does not occur are presented

blow up phenomena for a doubly degenerate equation with positive initial energy abstract in this paper an initial boundary value problem related to the equation u t div u m p 2 u m f u is studied under suitable conditions on f we establish a blow up result for certain solution with positive initial energy and blow up time will be also considered by using the differential inequality technique the upper estimate of the blow up solution near the single blow up point is also obtained

bounds for the blowup time of the solution to a parabolic system with nonlocal factors in nonlinearities in this paper we establish the lower and upper bounds for the blow up time of the solution to a system of parabolic equations u t u u r x t v s x t d x in 0 t v t v v q x t u p x t d x in 0 t subject to u x t v x t 0 on 0 t and nonnegative initial data under certain assumptions here r n is a smooth bounded open domain and n 3

very weak global solutions to a parabolic parabolic chemotaxis system with logistic source abstract in this paper we study this chemotaxis system u t u u v g u x t 0 v t v v u x t 0 defined in a convex smooth and bounded domain of r n with n 1 and endowed with homogeneous neumann boundary conditions being 0 and g a sort of logistic function obeying growth technical restrictions specifically once an appropriate definition of very weak solution is given our main result deals with the global existence of such solutions for any nonnegative initial data u 0 v 0 c 0 c 2 and under zero flux boundary condition on v 0

blow up phenomena in porous medium equation systems with nonlinear boundary conditions abstract this paper deals with the blow up phenomena for the following porous medium equation systems with nonlinear boundary conditions u t u m k 1 t f 1 v v t v n k 2 t f 2 u i n 0 t u g 1 u v g 2 v o n 0 t u x 0 u 0 x 0 v x 0 v 0 x 0 i n where m n 1 r n n 2 is bounded convex domain with smooth boundary using a differential inequality technique and a sobolev inequality we prove that under certain conditions on data the solution blows up in finite time we also derive an upper and a lower bound for blow up time in addition as applications of the abstract results obtained in this paper an example is given

global existence and blow up phenomena for nonlinear divergence form parabolic equations with inhomogeneous neumann boundary conditions abstract in this paper we consider nonlinear divergence form parabolic equations with inhomogeneous neumann boundary conditions we establish respectively the conditions on nonlinearities to guarantee that u x t exists globally or blows up at some finite time if blow up occurs we obtain upper and lower bounds of the blow up time

bounds for blow up time in a semilinear parabolic problem with viscoelastic term abstract we consider a semilinear parabolic equation with viscoelastic term u t u 0 t g t s u x s d s u p 2 u by the means of differential inequality technique we obtain a lower bound for blow up time of the solution if blow up occurs at the same time we establish a new blow up criterion and give an upper bound for blow up time of the solution under some conditions on p g and u 0

blow up solutions for reaction diffusion equations with nonlocal boundary conditions abstract we devote to investigating the following nonlinear reaction diffusion equations with nonlocal boundary conditions u t u u k 1 t f u in d 0 t u k 2 t d g u d x on d 0 t u x 0 u 0 x 0 in d where d is a bounded convex region in r n n 2 and the boundary d is smooth by constructing some auxiliary functions and using differential inequality technique we derive that the solution blows up at some finite time moreover upper and lower bounds of the blow up time are obtained

identification of channels with single and multiple inputs and outputs under linear constraints abstract the channel identification problem for multiple input multiple output mimo channels under linear constraints can be formulated as solving a linear system which involves finite dimensional gabor matrices and a pre determined unstructured matrix that represents the linear constraints while matrices of the latter type are fixed a priori by the constraints gabor matrices depend on the choice of their generating windows which is often chosen by the user this is important since even if the matrix associated with the linear constraints is ill conditioned the full system may be solvable if the windows are designed appropriately we prove that linear constraints consisting of a single equation always remove a single degree of freedom in the channel identification problem in the sense that preknowledge of such constraints allows identification of mimo channels with support size one greater than the fundamental limit however we give an explicit example showing that this statement does not generalize to the case of multiple constraints in the single input single output siso case we provide some sufficient conditions on the linear side constraints under which the corresponding siso channels are identifiable

blow up phenomena for a parabolic problem with a gradient nonlinearity under nonlinear boundary conditions this paper is concerned with the blow up of the solution to a parabolic problem with a gradient nonlinearity under nonlinear boundary conditions lower bound for blow up time is derived when the blow up does occur

lower bounds for blow up in a model of chemotaxis abstract many special cases of the classical keller segel system for modeling chemotaxis have been investigated in the literature and typically the solution of the governing equations will blow up at some finite time however the question of establishing lower bounds for this blow up time has been largely ignored this paper derives such a lower bound in a parabolic parabolic model in both r 2 and r 3

explicit lower bound of blow up time for an attraction repulsion chemotaxis system abstract in this paper we study classical solutions to the zero flux attraction repulsion chemotaxis system u t u u v u w in 0 t 0 v u v in 0 t 0 w u w in 0 t where is a smooth and bounded domain of r 2 t is the blow up time and are positive real numbers from the literature it is known that under a proper interplay between the above parameters and suitable assumptions on the initial data u x 0 u 0 c 0 system has a unique classical solution which becomes unbounded as t t the main result of this investigation is to provide an explicit lower bound for t estimated in terms of u 0 2 d x and attained by means of well established techniques based on ordinary differential inequalities

well posedness and long time behavior for p laplacian equation with nonlinear boundary condition abstract in this paper we study the homogeneous nonlinear boundary value problem for the p laplacian equation u t p u a x t u 2 u b x t u 2 u h x t we prove the existence of weak solutions which is global or local in time in dependence on the relation between the exponent of nonlinear part in boundary value and p boundedness of weak solution is proved we established conditions of uniqueness we prove also the properties of extinction in a finite time finite speed propagation and waiting time lastly by using the energy method we obtain sufficient conditions that the solutions of this problem with non positive initial energy blow up in finite time

boundedness in a chemotaxis model with oxygen consumption by bacteria abstract this paper deals with the keller segel model u t u u v x t 0 v t v u v x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r n n 2 with nonnegative initial data u 0 v 0 w 1 r 2 for some r n u 0 l 1 0 and v 0 l 0 this model describes bacteria movement toward the concentration gradient of the oxygen that is consumed by the bacteria it is proved that if 0 1 6 n 1 v 0 l then the corresponding initial boundary value problem possesses a unique global solution that is uniformly bounded

blow up phenomena for some nonlinear parabolic problems abstract we consider the blow up of solutions of equations of the form u t div u 2 grad u f u by means of a differential inequality technique a lower bound for blow up time is determined if blow up does occur as well as a criterion for blow up and conditions which ensure that blow up cannot occur

blow up and decay criteria for a model of chemotaxis for a system of equations introduced by jager and luckhaus 1992 6 as a model of chemotaxis the questions of blow up and global existence criteria are investigated specifically for a convex region a lower bound for the blow up time is derived if the solution blows up and explicit criteria to ensure non blow up are determined

on explosions of solutions to a system of partial differential equations modelling chemotaxis a system of partial differential equations modelling chemotactic aggregation is analysed keller segel model conditions on the system of paramaters are given implying global existence of smooth solutions in two space dimensions and radially symmetric situations explosion of the bacteria concentration in finite time is shown for a class of initial values

spin block persistence at finite temperature we explore a new definition of the persistence exponent measuring the probability that a spin never flips after a quench of an ising like model at a temperature while the usual definition only makes sense at t 0 this probability is now defined for spin blocks and a general scaling for it involving time and block linear size is introduced and illustrated by extensive simulations

global solution and blow up of a semilinear heat equation with logarithmic nonlinearity abstract we study the initial boundary value problem of a semilinear heat equation with logarithmic nonlinearity by using the logarithmic sobolev inequality and a family of potential wells we obtain the existence of global solution and blow up at under some suitable conditions on the other hand the results for decay estimates of the global solutions are also given our result in this paper means that the polynomial nonlinearity is a critical condition of blow up in finite time for the solutions of semilinear heat equations

nature versus nurture predictability in low temperature ising dynamics consider a dynamical many body system with a random initial state subsequently evolving through stochastic dynamics what is the relative importance of the initial state nature versus the realization of the stochastic dynamics nurture in predicting the final state we examined this question for the two dimensional ising ferromagnet following an initial deep quench from t ensuremath infty to t 0 we performed monte carlo studies on the overlap between identical twins raised in independent dynamical environments up to size l 500 our results suggest an overlap decaying with time as t ensuremath ensuremath theta h with ensuremath theta h 0 22 ifmmode pm else textpm fi 0 02 the same exponent holds for a quench to low but nonzero temperature this heritability exponent may equal the persistence exponent for the two dimensional ising ferromagnet but the two differ more generally

a refined criterion and lower bounds for the blow up time in a parabolic elliptic chemotaxis system with nonlinear diffusion abstract this paper deals with unbounded solutions to the following zero flux chemotaxis system u t u m 1 1 u u u m 2 2 v x t 0 t m a x 0 v m u x t 0 t m a x where 0 is a smooth and bounded domain of r n with n 1 t 0 t m a x is t m a x the blow up time and m 1 m 2 are real numbers given a sufficiently smooth initial data u 0 u x 0 0 and set m 1 u 0 x d x from the literature it is known that under a proper interplay between the above parameters m 1 m 2 and the extra condition v x t d x 0 system possesses for any 0 a unique classical solution which becomes unbounded at t t m a x in this investigation we first show that for p 0 n 2 m 2 m 1 any blowing up classical solution in l norm blows up also in l p 0 norm then we estimate the blow up time t m a x providing a lower bound t

exact exponent for the number of persistent spins in the zero temperature dynamics of the one dimensional potts model for the zero temperature glauber dynamics of theq state potts model the fractionr q t of spins which never flip up to timet decays like a power lawr q t t q when the initial condition is random by mapping the problem onto an exactly soluble one species coagulation model a a a or alternatively by transforming the problem into a free fermion model we obtain the exact expression of q for all values ofq the exponent q is in general irrational 3 0 53795082 4 0 63151575 with the exception ofq 2 andq for which 2 3 8 and 1

lower bounds for blow up time in parabolic problems under dirichlet conditions we consider an initial boundary value problem for the semilinear heat equation whose solution may blow up in finite time we use a differential inequality technique to determine a lower bound on blow up time if blow up occurs a second method based on a comparison principle is also presented

sampling and reconstruction of operators we study the recovery of operators with a bandlimited kohn nirenberg symbol from the action of such operators on a weighted impulse train a procedure we refer to as sampling of operators kailath bello and later kozek and the authors have shown that the sampling of operators is possible if the symbol of the operator is bandlimited to a set with area less than one in this paper we develop the theory of the sampling of operators in analogy with the classical theory of sampling of bandlimited functions we define the notions of sampling set and sampling rate for operators and give necessary and sufficient conditions on the sampling rate that depend on the size and geometry of the bandlimiting set we develop explicit reconstruction formulas for operator sampling that generalize reconstruction formulas for bandlimited functions we give necessary and sufficient conditions on the bandlimiting set under which sampling of operators is possible by their action on a given periodically weighted delta train we show that under mild geometric conditions on the bandlimiting set classes of operators are bandlimited to an unknown set of area less than one half permit sampling and reconstruction we generalize two results of the heckel and bolcskei concerning sampling of operators with area not greater than one half and less than one respectively by finding a larger class of operators to which they apply operators with bandlimited symbols have been used to model doubly dispersive communication channels with slowly time varying impulse response the results in this paper are rooted in work by bello and kailath in the 1960s

bounds for the blowup time and blowup rate estimates for a type of parabolic equations with weighted source abstract in this paper we will consider the blowup phenomena for a type of parabolic equations with weighted nonlinear source we obtain the estimates of the blowup rate and the bounds for blowup time of the solution to the problem in any smooth bounded domain r n n 3 in some special cases we can even get the exact values of blowup rate and blowup time

estimates for the blowup time of a combustion model with nonlocal heat sources abstract in this paper we establish the lower and upper bounds for the blowup time of the solution to a system of parabolic equations with nonlocal nonlinearities which appears in a model of combustion different techniques are applied to deal with the problems in different space dimensions we also discuss non simultaneous blowup phenomenon of the solution

finite time blow up of solutions to a cancer invasion mathematical model with haptotaxis effects abstract this paper considers the nonlinear system of cancer invasion model with haptotaxis effects in a bounded domain r n under the homogeneous neumann and robin type boundary conditions this model also includes the growth and decay effects of cancer cells normal cells and matrix degrading enzymes this study devoted to estimate the lower bounds for the finite time blow up of non negative solutions of the given cancer invasion system using first order differential inequality techniques and certain inequalities

blow up and global solutions for a class of nonlinear reaction diffusion equations under dirichlet boundary conditions abstract in this paper we consider the following reaction diffusion equations under dirichlet boundary condition g u t u 2 u k t f u in 0 t u x t 0 on 0 t u x 0 u 0 x 0 in where is a bounded domain of r n n 2 with smooth boundary by constructing some appropriate auxiliary functions and using a first order differential inequality technique the upper and lower bounds on blow up time when blow up occurs are presented moreover conditions on the data to ensure that the solution exists globally or blows up at some finite time are also derived

lower bounds for blow up time in a nonlinear parabolic problem abstract for a parabolic problem with a gradient nonlinearity which was introduced by chipot and weissler m chipot f b weissler some blow up results for a nonlinear parabolic problem with a gradient term siam j math anal 20 1989 886 907 see also b kawohl l a peletier observations on blow up and dead cores for nonlinear parabolic equations math z 202 1989 207 217 the question of blow up is investigated specifically if the solution blows up a lower bound for the time of blow up is derived

measurement of time variant linear channels the goal of channel measurement or operator identification is to obtain complete knowledge of a channel operator by observing the image of a finite number of input signals in this paper it is shown that the spreading support of the operator that is the support of the symplectic fourier transform of the kohn nirenberg symbol of the operator has area less than one then the operator is identifiable if the spreading support is larger than one then the operator is not identifiable the shape of the support region is essentially arbitrary thereby proving a conjecture of bello the input signal considered is a weighted delta train where the weights are the window function of a finite gabor system whose elements satisfy a certain robust completeness property

global existence of solutions for a strongly coupled quasilinear parabolic system we are interested in existence uniqueness and a priori estimates of non negative solutions to the following problem begin gathered u t delta left left 1 alpha v right u right uf u v hfill v t delta v vg u v quad in 0 infty times omega hfill u v 0 quad in 0 infty times partial omega hfill u 0 u 0 v 0 v 0 quad in omega hfill end gathered 1 0

blowup in diffusion equations a survey this paper deals with quasilinear reaction diffusion equations for which a solution local in time exists if the solution ceases to exist for some finite time we say that it blows up in contrast to linear equations blowup can occur even if the data are smooth and well defined for all times depending on the equation either the solution or some of its derivatives become singular we shall concentrate on those cases where the solution becomes unbounded in finite time this can occur in quasilinear equations if the heat source is strong enough there exist many theoretical studies on the question on the occurrence of blowup in this paper we shall recount some of the most interesting criteria and most important methods for analyzing blowup the asymptotic behavior of solutions near their singularities is only completely understood in the special case where the source is a power a better knowledge would be useful also for their numerical treatment thus not surprisingly the numerical analysis of this type of problems is still at a rather early stage the goal of this paper is to collect some of the known results and algorithms and to direct the attention to some open problems

damage spreading and critical exponents for model a ising dynamics using damage spreading and heat bath dynamics we study the ising model in 2 and 3 dimensions with non conservative dynamics our algorithm differs in some important points from previous ones which makes it rather efficient we give estimates for the exponent z which seem to be the most precise published so far 2 172 0 006 for d 2 2 032 0 004 for d 3 we also give precise estimates of the exponent introduced by janssen et al z phys b 73 1989 539 and of analogous but in principle independent exponents we find surprisingly that some of the latter agree with and give an explanation for this

blow up time estimate for a degenerate diffusion equation with gradient absorption this paper deals with a degenerate nonlinear diffusion equation with gradient absorption we at first determine finite time blow up of solutions both in the l norm and an integral measure and then estimate a lower bound of the blow up time by using the differential inequality technique it is mentioned that the blowing up of solutions to nonlinear pdes is usually defined in the l norms while the lower bounds of blow up time are all determined via some measures in the form of energy integrals so in general to estimate the lower bounds of blow up time it has to be assumed that the solutions do blow up in finite time with the involved integral measure before establishing their lower bounds of blow up time such assumptions are unnecessary in this paper

upper bound estimate for the blow up time of an evolution m laplace equation involving variable source and positive initial energy in this paper we study an evolution m laplace equation involving variable source and positive initial energy we establish a blow up result for a certain solution with positive initial energy and estimate the upper bound of the blow up time for the blowing up solutions

lower bounds for the blow up time in a temperature dependent navier stokes flow abstract in this paper we consider two different initial boundary value problems in temperature dependent viscous flow when the temperature equation has a nonlinear heat source term when blow up occurs we derive lower bounds for the blow up time in each case

identification of domain walls in coarsening systems at finite temperature recently b derrida phys rev e 55 3705 1997 introduced a numerical technique that allows one to measure the fraction of persistent spins in a coarsening nonequilibrium system at finite temperature in the present work we extend this method in a way that domain walls can be clearly identified to this end we consider three replicas instead of two as an application we measure the surface area of coarsening domains in the two dimensional ising model at finite temperature we also discuss the question of to what extent the results depend on the algorithmic implementation

non trivial exponents in the zero temperature dynamics of the 1d ising and potts models we consider the glauber dynamics of the q state potts model in one dimension at zero temperature starting with a random initial configuration we measure the density r t of spins which have never flipped from the beginning of the simulation until time t we find that for large t the density r t has a power law decay left r t sim t theta right where the exponent theta varies with q our simulations lead to theta simeq 37 for q 2 theta simeq 53 for q 3 and theta longrightarrow 1 as q longrightarrow infty

blow up phenomena for the nonlinear nonlocal porous medium equation under robin boundary condition in this paper we determine a lower bound for the blow up time of the nonlinear nonlocal porous medium equation under robin boundary condition if the solution blows up the conditions which ensure that the blow up does not occur are also presented