an efficient threshold dynamics method for wetting on rough surfaces the threshold dynamics method developed by merriman bence and osher mbo is an efficient method for simulating the motion by mean curvature flow when the interface is away from the solid boundary direct generalization of mbo type methods to the wetting problem with interfaces intersecting the solid boundary is not easy because solving the heat equation in a general domain with a wetting boundary condition is not as efficient as it is with the original mbo method the dynamics of the contact point also follows a different law compared with the dynamics of the interface away from the boundary in this paper we develop an efficient volume preserving threshold dynamics method for simulating wetting on rough surfaces this method is based on minimization of the weighted surface area functional over an extended domain that includes the solid phase the method is simple stable with o n log n complexity per time step and is not sensitive to the inhomogeneity or roughness of the solid boundary

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

threshold dynamics for the piecewise constant mumford shah functional we propose an efficient algorithm for minimizing the piecewise constant mumford shah functional of image segmentation it is based on the threshold dynamics of merriman bence and osher for evolving an interface by its mean curvature we show that a very fast minimization can be achieved by alternating the solution of a linear parabolic partial differential equation and simple thresholding

the dynamics of a fisher kpp nonlocal diffusion model with free boundaries abstract we introduce and study a class of free boundary models with nonlocal diffusion which are natural extensions of the free boundary models in 16 and elsewhere where local diffusion is used to describe the population dispersal with the free boundary representing the spreading front of the species we show that this nonlocal problem has a unique solution defined for all time and then examine its long time dynamical behavior when the growth function is of fisher kpp type we prove that a spreading vanishing dichotomy holds though for the spreading vanishing criteria significant differences arise from the well known local diffusion model in 16

entire solutions of time periodic fisher kpp equation on the half line abstract we study the entire solutions of the fisher kpp equation of the form u t u x x f t u on 0 with boundary condition u t 0 0 where f t u is a fisher kpp type of nonlinearity t periodic in t we obtain two types of entire solutions i for any c 2 a with a 1 t 0 t f u s 0 d s we obtain an entire solution u c t x connecting the periodic traveling wave solution c t x c t at t with the periodic solution v t x at t ii the second type of entire solution u t x connecting the solution of the initial problems of ode t f t at t and v t x at t with properties u x x 0 and u t p t where p t is the periodic solution of t f t

the variational multiscale method a paradigm for computational mechanics abstract we present a general treatment of the variational multiscale method in the context of an abstract dirichlet problem we show how the exact theory represents a paradigm for subgrid scale models and a posteriori error estimation we examine hierarchical p methods and bubbles in order to understand and ultimately approximate the fine scale green s function which appears in the theory we review relationships between residual free bubbles element green s functions and stabilized methods these suggest the applicability of the methodology to physically interesting problems in fluid mechanics acoustics and electromagnetics

global minimization for continuous multiphase partitioning problems using a dual approach this paper is devoted to the optimization problem of continuous multi partitioning or multi labeling which is based on a convex relaxation of the continuous potts model in contrast to previous efforts which are tackling the optimal labeling problem in a direct manner we first propose a novel dual model and then build up a corresponding duality based approach by analyzing the dual formulation sufficient conditions are derived which show that the relaxation is often exact i e there exists optimal solutions that are also globally optimal to the original nonconvex potts model in order to deal with the nonsmooth dual problem we develop a smoothing method based on the log sum exponential function and indicate that such a smoothing approach leads to a novel smoothed primal dual model and suggests labelings with maximum entropy such a smoothing method for the dual model also yields a new thresholding scheme to obtain approximate solutions an expectation maximization like algorithm is proposed based on the smoothed formulation which is shown to be superior in efficiency compared to earlier approaches from continuous optimization numerical experiments also show that our method outperforms several competitive approaches in various aspects such as lower energies and better visual quality

entire solutions in bistable reaction diffusion equations with nonlocal delayed nonlinearity this paper is concerned with entire solutions for bistable reaction diffusion equations with nonlocal delay in one dimensional spatial domain here the entire solutions are defined in the whole space and for all time t r assuming that the equation has an increasing traveling wave solution with nonzero wave speed and using the comparison argument we prove the existence of entire solutions which behave as two traveling wave solutions coming from both ends of the x axis and annihilating at a finite time furthermore we show that such an entire solution is unique up to space time translations and is liapunov stable a key idea is to characterize the asymptotic behavior of the solutions as t in terms of appropriate subsolutions and supersolutions in order to illustrate our main results two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are considered

spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity abstract this paper is concerned with the spreading speeds and traveling wave solutions of a nonlocal dispersal equation with degenerate monostable nonlinearity we first prove that the traveling wave solution with critical minimal speed c c decays exponentially as while other traveling wave solutions with c c do not decay exponentially as then the monotonicity and uniqueness up to translation of traveling wave solution with critical minimal speed is established finally we prove that the critical minimal wave speed c coincides with the asymptotic speed of spread

travelling fronts and entire solutions of the fisher kpp equation in ℝn this paper is devoted to time global solutions of the fisher kpp equation in n where f is a c 2 concave function on 0 1 such that f 0 f 1 0 and f 0 on 0 1 it is well known that this equation admits a finite dimensional manifold of planar travelling fronts solutions by considering the mixing of any density of travelling fronts we prove the existence of an infinite dimensional manifold of solutions in particular there are infinite dimensional manifolds of nonplanar travelling fronts and radial solutions furthermore up to an additional assumption a given solution u can be represented in terms of such a mixing of travelling fronts

an efficient iterative thresholding method for image segmentation abstract we proposed an efficient iterative thresholding method for multi phase image segmentation the algorithm is based on minimizing piecewise constant mumford shah functional in which the contour length or perimeter is approximated by a non local multi phase energy the minimization problem is solved by an iterative method each iteration consists of computing simple convolutions followed by a thresholding step the algorithm is easy to implement and has the optimal complexity o n log n per iteration we also show that the iterative algorithm has the total energy decaying property we present some numerical results to show the efficiency of our method

how to approximate the heat equation with neumann boundary conditions by nonlocal diffusion problems we present a model for nonlocal diffusion with neumann boundary conditions in a bounded smooth domain prescribing the flux through the boundary we study the limit of this family of nonlocal diffusion operators when a rescaling parameter related to the kernel of the nonlocal operator goes to zero we prove that the solutions of this family of problems converge to a solution of the heat equation with neumann boundary conditions

a multiphase level set framework for image segmentation using the mumford and shah model we propose a new multiphase level set framework for image segmentation using the mumford and shah model for piecewise constant and piecewise smooth optimal approximations the proposed method is also a generalization of an active contour model without edges based 2 phase segmentation developed by the authors earlier in t chan and l vese 1999 in scale space 99 m nilsen et al eds lncs vol 1682 pp 141 151 and t chan and l vese 2001 ieee ip 10 2 266 277 the multiphase level set formulation is new and of interest on its own by construction it automatically avoids the problems of vacuum and overlaps it needs only log n level set functions for n phases in the piecewise constant cases it can represent boundaries with complex topologies including triple junctionss in the piecewise smooth case only two level set functions formally suffice to represent any partition based on the four color theorem finally we validate the proposed models by numerical results for signal and image denoising and segmentation implemented using the osher and sethian level set method

traveling waves for a nonlocal dispersal sir model with delay and external supplies this paper is concerned with the existence nonexistence and minimal wave speed of traveling waves of a nonlocal dispersal delayed sir model with constant external supplies and holling ii incidence rate we find that the existence and nonexistence of traveling waves of the system are not only determined by the minimal wave speed c but also by the so called basic reproduction number r 0 of the corresponding reaction system that is we establish the existence of traveling waves for r 0 1 and each wave speed c c and the nonexistence for r 0 1 and any 0 c c or r 0 1 we also discuss how the latency of infection and the spatial movement of the infective individuals affect the minimal wave speed biologically speaking the longer the latency of infection in a vector is the slower the disease spreads

curve evolution implementation of the mumford shah functional for image segmentation denoising interpolation and magnification we first address the problem of simultaneous image segmentation and smoothing by approaching the mumford shah 1989 paradigm from a curve evolution perspective in particular we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours each gradient step involves solving an optimal estimation problem for the data within each region connecting curve evolution and the mumford shah functional with the theory of boundary value stochastic processes the resulting active contour model offers a tractable implementation of the original mumford shah model i e without resorting to elliptic approximations which have traditionally been favored for greater ease in implementation to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner various implementations of this algorithm are introduced to increase its speed of convergence we also outline a hierarchical implementation of this algorithm to handle important image features such as triple points and other multiple junctions next by generalizing the data fidelity term of the original mumford shah functional to incorporate a spatially varying penalty we extend our method to problems in which data quality varies across the image and to images in which sets of pixel measurements are missing this more general model leads us to a novel pde based approach for simultaneous image magnification segmentation and smoothing thereby extending the traditional applications of the mumford shah functional which only considers simultaneous segmentation and smoothing

global asymptotics in some quasimonotone reaction diffusion systems with delays abstract both dichotomy and trichotomy on the global asymptotics of some quasimonotone reaction diffusion systems with delays are established in terms of the principal eigenvalue of linear weakly coupled elliptic systems applications to a class of delayed reaction diffusion models of single species growth and to a reaction diffusion system with delay modelling the spread of bacterial infections are provided

entire solutions originating from multiple fronts of an epidemic model with nonlocal dispersal and bistable nonlinearity abstract this paper is concerned with the entire solutions of a nonlocal dispersal epidemic model which arises from the spread of fecally orally transmitted diseases under bistable assumptions it is well known that this model has three different types of traveling wave fronts the annihilating front and merging front entire solutions originating from two fronts of the system have also been constructed in 38 we first prove the uniqueness liapunov stability and continuous dependence on shift parameters of annihilating front entire solutions obtained in 38 a positive time derivative estimate for such entire solution is also obtained then we establish the existence of two different types of entire solutions merging three different fronts furthermore we show that these entire solutions are global lipschitz continuous with respect to the spatial variable x to the best of our knowledge it is the first time that the entire solutions originating from three fronts of diffusion systems have been constructed

existence uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal this paper is concerned with a nonlocal evolution equation which is used to model the spatial dispersal of organisms we study the existence uniqueness and stability of the positive steady solution for this nonlocal evolution equation under general conditions the global dynamics are also investigated and a trichotomy of the global asymptotics is established

transition semi wave solutions of reaction diffusion equations with free boundaries abstract in this paper we define the transition semi wave solution cf definition 1 1 of the following reaction diffusion equation with free boundaries 1 u t u x x f t x u t r x h t u t h t 0 t r h t u x t h t t r in the homogeneous case i e f t x u f u under the hypothesis f u c 1 0 1 f 0 f 1 0 f 1 0 f u 0 for u 1 we prove that the semi wave connecting 1 and 0 of 1 is unique provided it exists furthermore we prove that any bounded transition semi wave connecting 1 and 0 is exactly the semi wave in the cases where f is kpp fisher type and almost periodic in time space i e f t x u u c t u resp u a x u with c t resp a x being almost periodic applying totally different method we also prove any bounded transition semi wave connecting the unique almost periodic positive solution of u t u c t u resp u x x u a x u 0 and 0 is exactly the unique almost periodic semi wave of 1 finally we provide an example of the heterogeneous equation to show the existence of the transition semi wave without any global mean speeds

preconditioning techniques for large linear systems a survey this article surveys preconditioning techniques for the iterative solution of large linear systems with a focus on algebraic methods suitable for general sparse matrices covered topics include progress in incomplete factorization methods sparse approximate inverses reorderings parallelization issues and block and multilevel extensions some of the challenges ahead are also discussed an extensive bibliography completes the paper

a new petrov galerkin smoothed aggregation preconditioner for nonsymmetric linear systems we propose a new variant of smoothed aggregation sa suitable for nonsymmetric linear systems the new algorithm is based on two key generalizations of sa restriction smoothing and local damping restriction smoothing refers to the smoothing of a tentative restriction operator via a damped jacobi like iteration restriction smoothing is analogous to prolongator smoothing in standard sa and in fact has the same form as the transpose of prolongator smoothing when the matrix is symmetric local damping refers to damping parameters used in the jacobi like iteration in standard sa a single damping parameter is computed via an eigenvalue computation here local damping parameters are computed by considering the minimization of an energy like quantity for each individual grid transfer basis function numerical results are given showing how this method performs on highly nonsymmetric systems

performance of fully coupled algebraic multigrid preconditioners for large scale vms resistive mhd abstract this work explores the current performance and scaling of a fully implicit stabilized unstructured finite element fe variational multiscale vms capability for large scale simulations of 3d incompressible resistive magnetohydrodynamics mhd the large scale linear systems that are generated by a newton nonlinear solver approach are iteratively solved by preconditioned krylov subspace methods the efficiency of this approach is critically dependent on the scalability and performance of the algebraic multigrid preconditioner this study considers the performance of the numerical methods as recently implemented in the second generation trilinos implementation that is 64 bit compliant and is not limited by the 32 bit global identifiers of the original epetra based trilinos the study presents representative results for a poisson problem on 1 6 million cores of an ibm blue gene q platform to demonstrate very large scale parallel execution additionally results for a more challenging steady state mhd generator and a transient solution of a benchmark mhd turbulence calculation for the full resistive mhd system are also presented these results are obtained on up to 131 000 cores of a cray xc40 and one million cores of a bg q system

entire solutions for a multi type sis nonlocal epidemic model in r or z abstract in this paper we study entire solutions for a multi type sis nonlocal epidemic model in r or z the existence and asymptotic behavior of spatially independent solutions are first established some new entire solutions are then constructed by combining traveling wave fronts with different speeds and a spatially independent solution from the viewpoint of epidemiology the results provide some new spread ways of the epidemic

existence and uniqueness of entire solutions for a reaction diffusion equation abstract we consider entire solutions of u t u xx f u i e solutions that exist for all x t r 2 where f 0 f 1 0 f 0 in particular we are interested in the entire solutions which behave as two opposite wave fronts of positive speed s approaching each other from both sides of the x axis and then annihilating in a finite time in the case f 1 0 we show that such entire solution exists and is unique up to space time translations in the case f 1 0 we derive two families of such entire solutions in the first family one cannot be any space time translation of the other yet all entire solutions in the second family only differ by a space time translation

an integrodifferential model for phase transitions stationary solutions in higher space dimensions we study the existence and stability of stationary solutions of an integrodifferential model for phase transitions which is a gradient flow for a free energy functional with general nonlocal integrals penalizing spatial nonuniformity as such this model is a nonlocal extension of the allencahn equation which incorporates long range interactions we find that the set of stationary solutions for this model is much larger than that of the allencahn equation

the periodic principal eigenvalues with applications to the nonlocal dispersal logistic equation abstract in this paper we study the nonlocal dispersal equation u t r n j x y u y t d y u u a x t u p in 0 u x t 0 in r n 0 u x 0 u 0 x in where r n is a bounded domain and p 1 are constants the dispersal kernel j is nonnegative the function a c r is nonnegative and t periodic in t but a x t has temporal or spatial degeneracies a x t vanishes we first study the periodic nonlocal eigenvalue problems with parameter and establish the asymptotic behavior of principal eigenvalues when the parameter is large we find that the spatial degeneracy of a x t always guarantees a principal eigenfunction then we consider the dynamical behavior of the equation if a x t has temporal or spatial degeneracies our results indicate that only the temporal degeneracy can not cause a change of the dynamical behavior but the spatial degeneracy always causes fundamental changes whether or not the temporal degeneracy appears

traveling waves for a nonlocal anisotropic dispersal equation with monostable nonlinearity abstract this paper is concerned with traveling wave solutions of the equation u t j u u f u on r 0 where the dispersion kernel j is nonnegative and the nonlinearity f is monostable type we show that there exists c r such that for any c c there is a nonincreasing traveling wave solution with 1 and lim e 1 where 1 c is the smallest positive solution to c r j z e z d z 1 f 0 furthermore the existence of traveling wave solutions with c c is also established for c 0 we further prove that the traveling wave solution is unique up to translation and is globally asymptotically stable in certain sense

travelling wave fronts in reaction diffusion systems with spatio temporal delays this paper deals with the existence of travelling wave fronts in reaction diffusion systems with spatio temporal delays our approach is to use monotone iterations and a nonstandard ordering for the set of profiles of the corresponding wave system new iterative techniques are established for a class of integral operators when the reaction term satisfies different monotonicity conditions following this the existence of travelling wave fronts for reaction diffusion systems with spatio temporal delays is established finally we apply the main results to a single species diffusive model with spatio temporal delay and obtain some existence criteria of travelling wave fronts by choosing different kernels

asymptotic behavior of traveling fronts and entire solutions for a periodic bistable competition diffusion system abstract this paper is concerned with a time periodic competition diffusion system u t u x x u r 1 t a 1 t u b 1 t v t 0 x r v t d v x x v r 2 t a 2 t u b 2 t v t 0 x r where u t x and v t x denote the densities of two competing species d 0 is some constant r i t a i t and b i t are t periodic continuous functions under suitable conditions it has been confirmed by bao and wang 2013 2 that this system admits periodic traveling fronts connecting two stable semi trivial t periodic solutions p t 0 and 0 q t associated to the corresponding kinetic system in the present work we first investigate the asymptotic behavior of periodic bistable traveling fronts with non zero speeds at infinity by a dynamical approach combined with the two sided laplace transform method with these asymptotic properties we then obtain some key estimates as a result by applying the super and subsolutions techniques as well as the comparison principle we establish the existence and various qualitative properties of the so called entire solutions defined for all time and the whole space which provides some new spreading ways other than periodic traveling waves for two strongly competing species interacting in a heterogeneous environment

the speed of propagation for kpp type problems ii general domains this paper is devoted to nonlinear propagation phenomena in general unbounded domains of rn for reaction diffusion equations with kolmogorov petrovsky piskunov kpp type nonlinearities this article is the second in a series of two and it is the follow up of the paper 7 which dealt which the case of periodic domains this paper is concerned with general domains and we give various definitions of the spreading speeds at large times for solutions with compactly supported initial data we study the relationships between these new notions and analyze their dependence on the geometry of the domain and on the initial condition some a priori bounds are proved for large classes of domains the case of exterior domains is also discussed in detail lastly some domains which are very thin at infinity and for which the spreading speeds are infinite are exhibited the construction is based on some new heat kernel estimates in such domains

a nonlocal dispersal equation arising from a selection migration model in genetics this paper is concerned with the existence uniqueness and asymptotic stability of positive steady states for a nonlocal dispersal equation arising from selection migration models in genetics due to the lack of compactness and regularity of the nonlocal operators many classical methods cannot be used directly to the nonlocal dispersal problems this motivates us to find new techniques we first establish a criterion on the stability and instability of steady states this result is effective to get a necessary condition to guarantee a positive steady state it also gives the uniqueness then we prove the existence of nontrivial solutions by the corresponding auxiliary equations and maximum principle finally we consider the dynamic behavior of the initial value problem

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

a nonlocal convection diffusion equation in this paper we study a nonlocal equation that takes into account convective and diffusive effects ut j u u g f u f u in rd with j radially symmetric and g not necessarily symmetric first we prove existence uniqueness and continuous dependence with respect to the initial condition of solutions this problem is the nonlocal analogous to the usual local convection diffusion equation ut u b f u in fact we prove that solutions of the nonlocal equation converge to the solution of the usual convection diffusion equation when we rescale the convolution kernels j and g appropriately finally we study the asymptotic behaviour of solutions as t when f u u q 1u with q 1 we find the decay rate and the first order term in the asymptotic regime

approximate the fokker planck equation by a class of nonlocal dispersal problems abstract this paper is concerned with an inhomogeneous nonlocal dispersal equation we study the limit of the re scaled problem of this nonlocal operator and prove that the solutions of the re scaled equation converge to a solution of the fokker planck equation uniformly we then analyze the nonlocal dispersal equation of an inhomogeneous diffusion kernel and find that the heterogeneity in the classical diffusion term coincides with the inhomogeneous kernel when the scaling parameter goes to zero

entire solutions in nonlocal dispersal equations with bistable nonlinearity abstract we consider entire solutions of nonlocal dispersal equations with bistable nonlinearity in one dimensional spatial domain a two dimensional manifold of entire solutions which behave as two traveling wave solutions coming from both directions is established by an increasing traveling wave front with nonzero wave speed furthermore we show that such an entire solution is unique up to space time translations and liapunov stable a key idea is to characterize the asymptotic behaviors of the solutions as t in terms of appropriate subsolutions and supersolutions we have to emphasize that a lack of regularizing effect occurs

on a nonlocal equation arising in population dynamics we study a one dimensional nonlocal variant of fisher s equation describing the spatial spread of a mutant in a given population and its generalization to the so called monostable nonlinearity the dispersion of the genetic characters is assumed to follow a nonlocal diffusion law modelled by a convolution operator we prove that as in the classical local problem there exist travelling wave solutions of arbitrary speed beyond a critical value and also characterize the asymptotic behaviour of such solutions at infinity our proofs rely on an appropriate version of the maximum principle qualitative properties of solutions and approximation schemes leading to singular limits

dynamics of a nonlocal dispersal sis epidemic model with neumann boundary conditions abstract in this paper we study a nonlocal dispersal susceptible infected susceptible sis epidemic model with neumann boundary condition where the spatial movement of individuals is described by a nonlocal convolution diffusion operator the transmission rate and recovery rate are spatially heterogeneous and the total population number is constant we first define the basic reproduction number r 0 and discuss the existence uniqueness and stability of steady states of the nonlocal dispersal sis epidemic model in terms of r 0 then we consider the impacts of the large diffusion rates of the susceptible and infectious populations on the persistence and extinction of the disease the obtained results indicate that the nonlocal movement of the susceptible or infectious individuals will enhance the persistence of the infectious disease in particular our analytical results suggest that the spatial heterogeneity tends to boost the spread of the infectious disease

super critical and critical traveling waves in a three component delayed disease system with mixed diffusion abstract this paper deals with traveling waves of a three component delayed disease system with mixed diffusion when the basic reproduction number of the corresponding spatial homogenous delayed differential system r 0 1 and the wave velocity c c c is critical velocity we obtain that the system admits a positive traveling wave solution when r 0 1 and c r or r 0 1 and c c we prove that the system has no positive traveling wave solutions our theoretical results may be conducive to disease prevention and control

entire solutions of a monostable age structured population model in a 2d lattice strip abstract this paper is concerned with the entire solutions for a monostable age structured population model in a 2d lattice strip i e solutions defined in the whole space and for all time t r in the quasi monotone case we first establish the existence and asymptotic behavior of solutions of the equation without j z variable combining traveling wave fronts with different speeds and a solution without j variable the existence and qualitative features of entire solutions are then proved in the non quasi monotone case we introduce two auxiliary quasi monotone equations and establish a comparison argument for the three systems some new entire solutions are then constructed by using the comparison argument the traveling wave fronts and a solution without j variable of the auxiliary equations

entire solutions for nonlocal dispersal equations with spatio temporal delay monostable case abstract this paper deals with entire solutions for a general nonlocal dispersal monostable equation with spatio temporal delay i e solutions that are defined in the whole space and for all time t r we first derive a particular model for a single species and show how such systems arise from population biology then we construct some new types of entire solutions other than traveling wave solutions and equilibrium solutions of the equation under consideration with quasi monotone and non quasi monotone nonlinearities various qualitative properties of the entire solutions are also investigated in particular the relationship between the entire solutions and the traveling wave fronts which they originated is considered our main arguments are based on the comparison principle the method of super and sub solutions and the construction of auxiliary control systems

threshold dynamics for networks with arbitrary surface tensions we present and study a new algorithm for simulating the n phase mean curvature motion for an arbitrary set of isotropic surface tensions the departure point is the threshold dynamics algorithm of merriman bence and osher for the two phase case a new energetic interpretation of this algorithm allows us to extend it in a natural way to the case of n phases for arbitrary surface tensions and arbitrary isotropic mobilities for a large class of surface tensions the algorithm is shown to be consistent in the sense that at every time step it decreases an energy functional that is an approximation in the sense of gamma convergence of the interfacial energy a broad range of numerical tests shows good convergence properties an important application is the motion of grain boundaries in polycrystalline materials it is also established that the above mentioned large class of surface tensions contains the read shockley surface tensions both in the two dimensional and three dimensional settings 2015 wiley periodicals inc

approximation of functional depending on jumps by elliptic functional via t convergence we show how it is possible to approximate the mumford shah see 29 image segmentation functional by elliptic functionals defined on sobolev spaces the heuristic idea is to consider functionals h u z with z ranging between 0 and 1 and related to the set k the minimizing zh are near to 1 in a neighborhood of the set k and far from the neighborhood they are very small the neighborhood shrinks as h for a similar approach to the problem compare kulkarni see 25 the approximation of h to takes place in a variational sense the de giorgi f convergence

spreading speeds and linear determinacy of time dependent diffusive cooperative competitive systems abstract the current paper is devoted to the study of spreading speeds and linear determinacy of diffusive cooperative competitive systems of the form u t t x a u t x f t u t x x h where h r n or z n a is a random or nonlocal dispersal operator in the cases h r n and is a discrete dispersal operator in the case h z n f t u is cooperative or competitive in u and is recurrent in t which includes f t u is periodic and almost periodic in t as special cases first the notion of spreading speed intervals for diffusive cooperative systems is introduced via the natural features of spreading speeds and some basic spreading properties are established next some principal lyapunov exponent and principal floquent bundle theory for linear cooperative systems of ordinary differential equations is developed which plays an important role in the study of spreading speeds of diffusive cooperative competitive systems with time dependence and is also of independent interest in terms of the principal lyapunov exponent and principal floquent bundle theory some upper and lower bounds for the spreading speed intervals for diffusive cooperative systems are then established under certain conditions it is proved that a diffusive cooperative system has a single spreading speed and is linearly determinant finally by transforming a diffusive competitive system to a diffusive cooperative system and applying established results for diffusive cooperative systems upper and lower bounds for the spreading speed intervals for diffusive competitive systems are obtained and linearly determinacy for such systems is discussed

a fast segmentation method based on constraint optimization and its applications intensity inhomogeneity and texture segmentation we propose a new constraint optimization energy and an iteration scheme for image segmentation which is connected to edge weighted centroidal voronoi tessellation ewcvt we show that the characteristic functions of the edge weighted voronoi regions are the minimizers may not unique of the proposed energy at each iteration we propose a narrow banding algorithm to accelerate the implementation which makes the proposed method very fast we generalize the cvt segmentation to hand intensity inhomogeneous and texture segmentation by incorporating the global and local image information into the energy functional compared with other approaches such as level set method the experimental results in this paper have shown that our approach greatly improves the calculation efficiency without losing segmentation accuracy

existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay this paper is concerned with the existence uniqueness and globally asymptotic stability of traveling wave fronts in the quasi monotone reaction advection diffusion equations with nonlocal delay under bistable assumption we construct various pairs of super and subsolutions and employ the comparison principle and the squeezing technique to prove that the equation has a unique nondecreasing traveling wave front up to translation which is monotonically increasing and globally asymptotically stable with phase shift the influence of advection on the propagation speed is also considered comparing with the previous results our results recovers and or improves a number of existing ones in particular these results can be applied to a reaction advection diffusion equation with nonlocal delayed effect and a diffusion population model with distributed maturation delay some new results are obtained

entire solutions of the kpp equation this paper deals with the solutions defined for all time of the kpp equation ut uxx f u 0 0 f 0 1 0i n 0 1 and f 0 s f 0 0 in 0 1 this equation admits infinitely many traveling wave type solutions increasing or decreasing in x i t also admits solutions that depend only on t in this paper we build four other manifolds of solutions one is 5 dimensional one is 4 dimensional and two are 3 dimensional some of these new solutions are obtained by considering two traveling waves that come from both sides of the real axis and mix furthermore the traveling wave solutions are on the boundary of these four manifolds c 1999 john wiley sons inc

entire solutions in monostable reaction diffusion equations with delayed nonlinearity abstract entire solutions for monostable reaction diffusion equations with nonlocal delay in one dimensional spatial domain are considered a comparison argument is employed to prove the existence of entire solutions which behave as two traveling wave solutions coming from both directions some new entire solutions are also constructed by mixing traveling wave solutions with heteroclinic orbits of the spatially averaged ordinary differential equations and the existence of such a heteroclinic orbit is established using the monotone dynamical systems theory key techniques include the characterization of the asymptotic behaviors of solutions as t in term of appropriate subsolutions and supersolutions two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are given to illustrate main results

boundary fluxes for nonlocal diffusion abstract we study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary this problem may be seen as a generalization of the usual neumann problem for the heat equation first we prove existence uniqueness and a comparison principle next we study the behavior of solutions for some prescribed boundary data including blowing up ones finally we look at a nonlinear flux boundary condition

multiclass data segmentation using diffuse interface methods on graphs we present two graph based algorithms for multiclass segmentation of high dimensional data on graphs the algorithms use a diffuse interface model based on the ginzburg landau functional related to total variation and graph cuts a multiclass extension is introduced using the gibbs simplex with the functional s double well potential modified to handle the multiclass case the first algorithm minimizes the functional using a convex splitting numerical scheme the second algorithm uses a graph adaptation of the classical numerical merriman bence osher mbo scheme which alternates between diffusion and thresholding we demonstrate the performance of both algorithms experimentally on synthetic data image labeling and several benchmark data sets such as mnist coil and webkb we also make use of fast numerical solvers for finding the eigenvectors and eigenvalues of the graph laplacian and take advantage of the sparsity of the matrix experiments indicate that the results are competitive with or better than the current state of the art in multiclass graph based segmentation algorithms for high dimensional data