convergence to equilibrium in a reaction diffusion system on etudie le comportement des solutions d un systeme d equations aux derivees partielles non lineaires paraboliques satisfaisant des conditions aux limites de neumann

exponential decay toward equilibrium via entropy methods for reaction diffusion equations abstract in this work we show how the entropy method enables to get in an elementary way and without linearization estimates of exponential decay towards equilibrium for solutions of reaction diffusion equations corresponding to a reversible reaction explicit rates of convergence combining the dissipative effects of diffusion and reaction are given

local multiplicity adjustment for the spatial scan statistic using the gumbel distribution the spatial scan statistic is an important and widely used tool for cluster detection it is based on the simultaneous evaluation of the statistical significance of the maximum likelihood ratio test statistic over a large collection of potential clusters in most cluster detection problems there is variation in the extent of local multiplicity across the study region for example using a fixed maximum geographic radius for clusters urban areas typically have many overlapping potential clusters while rural areas have relatively few the spatial scan statistic does not account for local multiplicity variation we describe a previously proposed local multiplicity adjustment based on a nested bonferroni correction and propose a novel adjustment based on a gumbel distribution approximation to the distribution of a local scan statistic we compare the performance of all three statistics in terms of power and a novel unbiased cluster detection criterion these methods are then applied to the well known new york leukemia dataset and a wisconsin breast cancer incidence dataset

a stability instability boundary for disturbance free slow adaptation with unmodeled dynamics the instability of adaptive schemes for small values of parameter adjustment gain has the form of a slow drift of adjustable parameters with an averaging analysis we derive not only a sufficient condition for stability of this drift but also a sufficient condition for it to be unstable a sharp boundary between stability and instability is signal dependent and much less demanding than the usual strict positive realness property the new positivity condition has a simple signal energy interpretation

global solutions to semilinear parabolic systems for small data abstract we consider semilinear parabolic systems u t au f u g u 0 u 0 a being the generator of an analytic semigroup with spectrum a in the right half plane for appropriate small data g u 0 global solutions are obtained if 0 belongs to the resolvent set and local existence is proved if 0 a the inverse function theorem is used in a class of functions which are holder continuous with respect to time t the asymptotic behaviour of the solution is given too as a first application we prove the existence of global respectively local solutions to the navier stokes equations in l spaces in bounded respectively unbounded domains second we consider the case where a is an elliptic operator of order 2 m and f has bounded growth third a quasilinear example where the nonlinearity involves derivatives of the same order as a is studied then an example of a nonautonomous nonlinearity is given and finally the convergence of solutions of the time dependent system to solutions of the stationary semilinear elliptic one is derived for 0 a

stability of slow adaptation for non spr systems with disturbances sufficient conditions are given for the existence of a bounded uniformly asymptotically stable u a s solution of the model reference adaptive control system these conditions which do not require any matching assumptions or knowledge of the order of the plant provide an estimate of the region of attraction and a bound on the average squared tracking error for which the u a s property of the solution is preserved

radial solutions and phase separation in a system of two coupled schrodinger equations we consider the nonlinear elliptic system left begin aligned delta u u u 3 beta v 2u 0 quad rm in mathbb b delta v v v 3 beta u 2v 0 quad rm in mathbb b u v 0 quad rm in mathbb b quad u v 0 quad rm on partial mathbb b end aligned right where n leqq 3 and mathbb b subset mathbb r n is the unit ball we show that for every beta leqq 1 and k in mathbb n the above problem admits a radially symmetric solution u v such that u v changes sign precisely k times in the radial variable furthermore as beta to infty after passing to a subsequence u w and v w uniformly in mathbb b where w w w has precisely k nodal domains and is a radially symmetric solution of the scalar equation w w w3 0 in mathbb b w 0 on partial mathbb b within a hartree fock approximation the result provides a theoretical indication of phase separation into many nodal domains for bose einstein double condensates with strong repulsion

asymptotic constancy for pseudo monotone dynamical systems on function spaces abstract a pseudo monotone dynamical system is a dynamical system which preserves the order relation between initial points and equilibrium points the purpose of this paper is to present some convergence oscillation and order stability criteria for pseudo monotone dynamical systems on function spaces for which each constant function is an equilibrium point some applications to neutral functional differential equations and semilinear parabolic partial differential equations with neumann boundary condition are given

parabolic evolution equations and nonlinear boundary conditions on etudie le probleme aux valeurs limites et initiales u 7b a t u f t u 7b b t u g t u 0 t t u 0 u 0 qui peut etre considere comme une contrepartie abstraite a des problemes paraboliques semilineaires

diffraction problems for quasilinear reaction diffusion systems abstract the aim of this paper is to investigate existence uniqueness and qualitative properties of the weak and piecewise classical solutions of the diffraction problem for weakly coupled reaction diffusion systems monotony and stability with respect to the time variable of the weak solutions is proved as an application is considered a model reaction diffusion system describing an enzyme sensor for concentration of phenol in the chemical industry

admissible lp norms for local existence and for continuation in semilinear parabolic systems are not the same we say that a banach space e is a continuation space for a given parabolic problem if the e norm of any non global solution has to become unbounded we will prove that for large classes of parabolic systems of two equations the space e l r 1 l r 2 can be a continuation space even though the problem is not locally well posed in e this stands in contrast with classical results for analogous scalar equations

global existence and nonexistence for semilinear parabolic systems with nonlinear boundary conditions on etudie des problemes aux valeurs limites et initiales paraboliques semilineaires de la forme t u j a jk k u a 0 u f u dans 0 a jk j k u bu 1 u g u sur 0 u 0 u 0 sur ou est un domaine borne de r n n 1 de classe c 2

global existence for coupled reaction diffusion systems abstract we prove here global existence in time of classical solutions for reaction diffusion systems with strong coupling in the diffusion and with natural structure conditions on the nonlinear reactive terms this extends some similar results in the case of a diagonal diffusion operator associated with nonlinearities preserving the positivity and the total mass of the solutions or for which the total mass is a priori bounded here however no positivity assumption is made since nondiagonal systems do not preserve it

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

a permutation characterization of sturm global attractors of hamiltonian type abstract we consider neumann boundary value problems of the form u t u x x f on the interval 0 x for dissipative nonlinearities f f u a permutation characterization for the global attractors of the semiflows generated by these equations is well known even in the much more general case f f x u u x we present a permutation characterization for the global attractors in the restrictive class of nonlinearities f f u in this class the stationary solutions of the parabolic equation satisfy the second order ode v f v 0 and we obtain the permutation characterization from a characterization of the set of 2 periodic orbits of this planar hamiltonian system our results are based on a diligent discussion of this mere pendulum equation

mixture of regression models for large spatial datasets abstractwhen a spatial regression model that links a response variable to a set of explanatory variables is desired it is unlikely that the same regression model holds throughout the domain when t

h optimization and optimal rejection of persistent disturbances abstract in this note it is shown that in a certain well known normed space of persistent signals a natural optimal disturbance rejection problem is equivalent to h optimization thus clarifying certain misconceptions on h optimization in the literature these conclusions are further strengthened using techniques of wiener s generalized harmonic analysis

asymptotic spatial homogeneity in periodic quasimonotone reaction diffusion systems with a first integral abstract the asymptotic spatial homogeneity of nonnegative solutions to a periodic quasimonotone reaction diffusion type initial boundary value problem is established provided the system possesses a first integral the infinite dimensional dynamical system generated by the system of pdes is monotone but not strongly monotone results combining simple monotonicity with infinite dimensionality have not appeared in the literature we apply our result to a cooperative lotka volterra system with spatial diffusion

global attractor for sectorial evolutionary equation an abstract differential equation with sectorial operator is shown to generate a dissipative semigroup whenever an appropriate introductory estimate for solutions is known based on hale s theory of dissipative systems such an a priori estimate is then shown to be sufficient for existence of a global attractor examples contained in the final part of the paper illustrate presented ideas 1996 academic press inc 1 introductory notes

fast subset scan for spatial pattern detection summary we propose a new fast subset scan approach for accurate and computationally efficient event detection in massive data sets we treat event detection as a search over subsets of data records finding the subset which maximizes some score function we prove that many commonly used functions e g kulldorff s spatial scan statistic and extensions satisfy the linear time subset scanning property enabling exact and efficient optimization over subsets in the spatial setting we demonstrate that proximity constrained subset scans substantially improve the timeliness and accuracy of event detection detecting emerging outbreaks of disease 2 days faster than existing methods

semigroups and nonlinear evolution equations abstract in the main part of this paper we survey some recent results on a semigroup approach to parabolic equations under nonlinear boundary conditions in particular we give a detailed motivation and a heuristic derivation of a generalized variation of constant formula which is the basis for the whole method in the appendix we prove some new results about semigroups in interpolation and extrapolation spaces

integral manifolds of slow adaptation conditions are given under which an integral manifold slow manifold exists for a nonlinear system representing a broad class of adaptive algorithms the parameter update equation restricted to the manifold is an exact description of the slow adaptation process which can be approximately analyzed by averaging stability properties of the slow motion in the manifold are extended off the manifold by a set of conditions under which the manifold is shown to be attractive this two time scale analysis provides a geometrical visualization of instability phenomena observed in adaptive systems and generalizes earlier local stability results

asymptotic behavior of strongly monotone time periodic dynamical processes with symmetry given a strongly monotone discrete time dynamical system tn x x n z in an open and order convex subset x of a separable strongly ordered banach space v and a compact connected metrizable group g whose action on x is monotone and commutes with t we prove under some reasonable additional hypotheses that the limit set x of every stable point x x consists of symmetric points only i e g w w for all w x and g g moreover the set of all unstable points is contained in a union of at most countably many lipschitz manifolds of codimension one in v where each manifold is invariant under t and the action of g this result is applied to the time periodic spatially independent irreducible cooperative system of n reaction diffusion equations u t d t u f t u for t x r1 rn with spatially periodic boundary conditions in rn and with an initial distribution u0 which is continuous and satisfies the boundary conditions if u0 is stable then u0 contains spatially constant functions only and the dynamics on u0 is given by the irreducible cooperative system of n odes dudt f t u for t r1 here t is the poincare map if n 1 then u0 is a single fixed point of t if n 2 then v0 is a single fixed point of t for each v0 u0

realization of meander permutations by boundary value problems abstract we consider neumann boundary value problems of the form uxx f x u ux 0 on the unit interval 0 x 1 for a certain class of dissipative nonlinearities f associated to these problems we have i meanders in the phase space u ux r 2 which are connected oriented simple curves on the plane intersecting a fixed oriented line the u axis in n points corresponding to the solutions and ii meander permutations f s n obtained by ordering the intersection points first along the u axis and then along the meander the meander permutation f is the permutation defined by the braid of solutions in the space x u ux it was recently shown by fiedler and rocha that f determines the global attractor of the dynamical system generated by the semilinear parabolic differential equation ut uxx f x u ux up to c0 orbit equivalence therefore these permutations are of considerable importance in the classification problem of the morse smale attractors for these dynamical systems in this paper we present a purely combinatorial characterization of the set of meander permutations that are realizable by the above boundary value problems

an asymptotic supnorm estimate for solutions of 1 d systems of convection diffusion equations abstract we show how to use the l p l q approach to obtain fundamental estimates for the spatial supnorm values of solutions u x t u 1 x t u m x t to general systems of convection diffusion equations of the form u i t x f i x t u 1 u m x g i t u i i t 2 u i x 2 1 i m with initial data u 0 l p 0 r l r for some 1 p 0 where i t 0 given arbitrary f f 1 f m g g 1 g m such that f x t u b t u for all x r t 0 u r m where b c 0 0

the entropy dissipation method for spatially inhomogeneous reaction diffusion type systems we study the large time asymptotics of reaction diusion type systems which feature a monotone decaying entropy lyapunov free energy functional we consider both bounded domains and conning potentials on the whole space for ar bitrary space dimensions our aim is to derive quantitative expressions for or estimates of the rates of convergence towards an entropy minimising equilibrium state in terms of the constants of diusion and reaction and with respect to con served quantities our method the so called entropy approach seeks to quantify convergence to equilibrium by using functional inequalities which relate quantita tively the entropy and its dissipation in time the entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model varia tions it has already been widely applied to scalar diusion convection equations and the main goal of this paper is to study its generalisation to systems of partial dierential equations which contain diusion and reaction terms and admit fewer conservation laws than the size of the system in particular we successfully ap ply the entropy approach to general linear systems and to a nonlinear example of reaction diusion convection system arising in solid state physics as a paradigm for general nonlinear systems

curvature flows on surfaces with boundary a theorem of r hamilton 6 and b chow states that for every initial metric the initial value problem 1 possesses a unique solution which is defined for all t 0 moreover for t the solution converges exponentially to a metric of constant gauss curvature different proofs for this result were given by j bartz m struwe and r ye 2 and by m struwe 13 on a surface with boundary one can demand that the gauss curvature in the interior is constant and the geodesic curvature at the boundary vanishes alternatively one can require that the geodesic curvature at the boundary is constant and the gauss curvature in the interior vanishes the evolution equation corresponding to the first case is

doubly nonlinear degenerate parabolic systems with coupled nonlinear boundary conditions in this paper we study the global existence and the global nonexistence of doubly nonlinear degenerate parabolic systems with nonlinear boundary conditions we first prove a local existence result by the regularization method next we construct a weak comparison principle then we discuss the large time behavior of solutions by using a modified upper and lower solution methods and constructing various upper and lower solutions necessary and sufficient conditions on the global existence of all positive weak solutions are obtained

quasilinear evolution equations and parabolic systems it is shown that general quasilinear parabolic systems possess unique maximal classical solutions for sufficiently smooth initial values provided the boundary conditions are time independent moreover it is shown that in the autonomous case these equations generate local semi flows on appropriate sobolev spaces our results apply in particular to the case of prescribed boundary values dirichlet boundary conditions

asymptotic behavior and attractors for reaction diffusion equations in unbounded domains abstract in this paper we give general and flexible conditions for a reaction diffusion equation to be dissipative in an unbounded domain the functional setting is based on standard lebesgue and sobolev lebesgue spaces we show how the reaction and diffusion mechanisms have to work together to obtain the asymptotic compactness of solutions and therefore the existence of the compact attractor in particular cases our results allow us to improve some previous known results

fast detection of arbitrarily shaped disease clusters disease cluster detection and evaluation have commonly used spatial statistics methods that scan the map with a fixed circular window to locate candidate clusters recently there has been interest in searching for clusters with arbitrary shape the circular scan test retains high power of detecting a cluster but does not necessarily identify the exact regions contained in a non circular cluster particularly well we propose implement and evaluate a new procedure that is fast and produces clusters estimates of arbitrary shape in a rich class of possible cluster candidates we showed that our methods contain the so called upper level set method as a particular case we present a power study of our method and among other results the main conclusion is that the likelihood based arbitrarily shaped scan method is not appropriate to find a cluster estimate when the parameter space includes the set of all possible spatial clusters in a map a large and discrete parameter space maximum likely cluster estimates tend to overestimate the true cluster by a large extent this calls for a new approach different from the maximum likelihood method for this important public health problem

the dynamics of rotating waves in scalar reaction diffusion equations on etudie l attracteur compact maximal pour l equation u t u xx f u u x avec des conditions aux limites periodiques on montre qu un ensemble limite contient une onde de rotation

on global existence for semilinear parabolic systems we present some results on global existence of classical solutions of certain semilinear parabolic systems with homogeneous dirichlet boundary conditions in bounded domains with a smooth boundary relaxing the usual monotonicity assumptions on the nonlinearities

quasi steady state approximation for a reaction diffusion system with fast intermediate abstract we consider a prototype reaction diffusion system which models a network of two consecutive reactions in which chemical components a and b form an intermediate c which decays into two products p and q such a situation often occurs in applications and in the typical case when the intermediate is highly reactive the species c is eliminated from the system by means of a quasi steady state approximation in this paper we prove the convergence of the solutions in l 2 as the decay rate of the intermediate tends to infinity for all bounded initial data even in the case of initial boundary layers the limiting system is indeed the one which results from formal application of the qssa the proof combines the recent l 2 approach to reaction diffusion systems having at most quadratic reaction terms with local l bounds which are independent of the decay rate of the intermediate we also prove existence of global classical solutions to the initial system

optimal control of a nutrient phytoplankton zooplankton fish system we consider the mathematical formulation analysis and numerical solution of an optimal control problem for a nonlinear nutrient phytoplankton zooplankton fish reaction diffusion system we study the existence of optimal solutions derive an optimality system and determine optimal solutions in the original spatially homogeneous formulation m scheffer oikos 62 1991 pp 271 282 the dynamics of plankton were investigated as a function of parameters for nutrient levels and fish predation rate on zooplankton in our paper the model is spatially extended and the parameter for fish predation treated as a multiplicative control variable the model has implications for the biomanipulation of food webs in eutrophic lakes to help improve water quality in order to illustrate the control of irregular spatiotemporal dynamics of plankton in the model we implement a semi implicit in time finite element method with mass lumping and present the results of numerical experiments in two space dimensions

local and global solutions for some parabolic nonlocal problems abstract we study local and global existence of solutions for some semilinear parabolic initial boundary value problems with autonomous nonlinearities having a newtonian nonlocal term

integral inequalities and global solutions of semilinear evolution equations a criterion for the nonexplosion of solutions to semilinear evolution equations on banach spaces is proved the result is obtained by applying a modification of the bihari type inequality to the case of a weakly singular nonlinear integral inequality

an elliptic spatial scan statistic the spatial scan statistic is commonly used for geographical disease cluster detection cluster evaluation and disease surveillance the most commonly used shape of the scanning window is circular in this paper we explore an elliptic version of the spatial scan statistic using a scanning window of variable location shape eccentricity angle and size and with and without an eccentricity penalty the method is applied to breast cancer mortality data from northeastern united states and female oral cancer mortality in the united states power comparisons are made with the circular scan statistic

bifurcation and stability of periodic traveling waves for a reaction diffusion system v plane having a stable critical point at 1 o and unstable critical points at 0 o and cos sin moreover if we take 0 rc then flows starting with 3 i rc make large excursions before decaying to 1 0 whereas those with 0 decay monotonically to l o this excitability is a feature in common with the nonlinear vector field in the hodgkin huxley equations and also with the simpler fitzhugh nagumo equations we begin by describing some results of numerical simulations we made of

close to equilibrium behaviour of quadratic reaction diffusion systems with detailed balance abstract we study general quadratic reaction diffusion systems with detailed balance in space dimension d 4 we show that close to equilibrium solutions in an l 2 sense are regular for all times and that they relax to equilibrium exponentially in a strong sense that is all detailed balance equilibria are exponentially asymptotically stable in all l p norms at least in dimension d 4 the results are given in detail for the four species reaction diffusion system where the involved constants can be estimated explicitly the main novelty is the regularity result and exponential relaxation in l p norms for p 1 which up to our knowledge is new in dimensions 3 and 4

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

global existence for semilinear parabolic systems on etudie des problemes aux valeurs limites et initiales paraboliques semilineaires de la forme u t a t u f t x u du d 2m 1 u dans t 0 b t u 0 sur t 0 u t 0 u 0 sur ou est un domaine de r n

cluster detection of spatial regression coefficients popular approaches to spatial cluster detection such as the spatial scan statistic are defined in terms of the responses here we consider a varying coefficient regression and spatial clusters in the regression coefficients for varying coefficient regression such as the geographically weighted regression different regression coefficients are obtained for different spatial units it is often of interest to the practitioners to identify clusters of spatial units with distinct patterns in a regression coefficient but there is no formal statistical methodology for that rather cluster identification is often ad hoc such as by eyeballing the map of fitted regression coefficients and discerning patterns in this paper we develop new methodology for spatial cluster detection in the regression setting based on hypotheses testing we evaluate our methods in terms of power and coverages for true clusters via simulation studies for illustration our methodology is applied to a cancer mortality dataset copyright 2016 john wiley sons ltd