blow up of solutions to semilinear wave equations with variable coefficients and boundary this paper is devoted to studying initial boundary value problems for semilinear wave equations and derivative semilinear wave equations with variable coefficients on exterior domain with subcritical exponents in n space dimensions we will establish blow up results for the initial boundary value problems it is proved that there can be no global solutions no matter how small the initial data are and also we give the life span estimate of solutions for the problems

spreading speeds and traveling waves for periodic evolution systems abstract the theory of spreading speeds and traveling waves for monotone autonomous semiflows is extended to periodic semiflows in the monostable case then these abstract results are applied to a periodic system modeling man environment man epidemics a periodic time delayed and diffusive equation and a periodic reaction diffusion equation on a cylinder

improved kato s lemma on ordinary differential inequality and its application to semilinear wave equations abstract we are interested in the upper bound of the lifespan of solutions of semilinear wave equations for the sub critical case in high dimensions it has been believed that the basic tools of its analysis are kato s lemma on ordinary differential inequalities and the rescaling argument in the functional method but there is a small lack of delicate analysis and no published paper about this here we give a simple alternative proof by means of improved kato s lemma without any rescaling argument

weighted strichartz estimates and global existence for semilinear wave equations in this paper we prove a sharp global existence theorem in all dimensions for nonlinear wave equations with power type nonlinearities the proof is based on a weighted strichartz estimate involving powers of the lorentz distance

an elementary proof of the blow up for semilinear wave equation in high space dimensions abstract this paper concerns the blow up of solutions to u tt u u p in high dimensions for n 4 and 1 p p 0 n where p 0 n is a critical exponent we proved that the solutions blow up in finite time by estimating the solutions near the wave front using elementary inequalities

an elementary proof of strauss conjecture abstract in this paper we consider the cauchy problem for semilinear wave equation in high dimensions first we use a morawetz energy estimate which is obtained by integrating on the light cone to get a weighted l 2 l 2 estimate of the solution and then give an elementary proof of the weighted strichartz estimate in georgiev et al 3 hence the strauss conjecture we also obtain a variant of the weighted strichartz estimates and give the sharp estimate of the lifespan for the semilinear wave equation with subcritical nonlinearity

finite time blow up for critical wave equations in high dimensions we prove that solutions to the critical wave equation 1 1 with dimension n 4 can not be global if the initial values are positive somewhere and nonnegative this completes the solution to the famous strauss conjecture about semilinear wave equations of the form u t2u u p 0 the rest of the cases the lower dimensional case n 3 and the sub or super critical cases were settled many years earlier by the work of several authors

a comparison of computational color constancy algorithms i methodology and experiments with synthesized data we introduce a context for testing computational color constancy specify our approach to the implementation of a number of the leading algorithms and report the results of three experiments using synthesized data experiments using synthesized data are important because the ground truth is known possible confounds due to camera characterization and pre processing are absent and various factors affecting color constancy can be efficiently investigated because they can be manipulated individually and precisely the algorithms chosen for close study include two gray world methods a limiting case of a version of the retinex method a number of variants of forsyth s 1990 gamut mapping method cardei et al s 2000 neural net method and finlayson et al s color by correlation method finlayson et al 1997 2001 hubel and finlayson 2000 we investigate the ability of these algorithms to make estimates of three different color constancy quantities the chromaticity of the scene illuminant the overall magnitude of that illuminant and a corrected illumination invariant image we consider algorithm performance as a function of the number of surfaces in scenes generated from reflectance spectra the relative effect on the algorithms of added specularities and the effect of subsequent clipping of the data all data is available on line at http www cs sfu ca spl sim color data and implementations for most of the algorithms are also available http www cs sfu ca spl sim color code

saddle point behavior for monotone semiflows and reaction diffusion models the saddle point behavior is established for monotone semiflows with weak bistability structure and then these results are applied to three reaction diffusion systems modeling man environment man epidemics single loop positive feedback and two species competition respectively

nonexistence of global solutions to semilinear wave equations in high dimensions on considere le probleme de cauchy pour l equation d onde semi lineaire 2 t 2 u x t u x t p p 1 u x o f x u t x o g x avec f g c o r n

on abstract strichartz estimates and the strauss conjecture for nontrapping obstacles we establish the strauss conjecture concerning small data global existence for nonlinear wave equations in the setting of exterior domains to compact obstacles for space dimensions n 3 and 4 the obstacle is assumed to be nontrapping and the solution is assumed to satisfy either dirichlet or neumann conditions along the boundary of the obstacle the key step in the proof is establishing certain abstract strichartz estimates for the linear wave equation on exterior domains

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

long time existence for small amplitude semilinear wave equations we prove that a certain class of semilinear wave equations has global solutions if the initial data is small these existence results rely on mixed norm angular radial space time estimates more specifically we consider power nonlinearities u f p u where f p u u p and 2 t denotes the d alembertian on inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i in 1979 john investigated this equation for small initial data in dimension n 3 he proved that if p 1 2 then there is a global solution whereas for p n dimensions and the critical power p c above which global solutions exist should be the positive root of n 1 p 2 c n 1 p c 2 0 sideris proved that for all n the solutions can blow up if p p c recently zhou proved that for n 4 one has global solutions if p p c 2 here we prove that for n 8 one has global solutions if p p c furthermore we proved that for all n one has global solutions if p p c and the initial data are spherically symmetric in the radial case we use l p estimates derived from the explicit form of the fundamental solution using inequalities from classical analysis in the nonradial case we write the fundamental solution in polar coordinates and use fourier integral and special function estimates to handle the angular part

finite time blow up to critical semilinear wave equation outside the ball in 3 d abstract in this paper we study the initial boundary value problem of critical semilinear wave equation with small initial data in 3 d blow up result will be established no matter how small the data are we find a radial and positive solution of the corresponding linear problem then our blow up result follows from the idea of zhou and han 2014 what is more we get the upper bound of the lifespan estimate

concerning the strauss conjecture on asymptotically euclidean manifolds abstract in this paper we verify the strauss conjecture for semilinear wave equations on asymptotically euclidean manifolds when n 3 4 we also give an almost sharp lifespan for the subcritical case 2 p p c when n 3 the main ingredients include a keel smith sogge type estimate with 0 1 2 and weighted strichartz estimates of order two

a novel algorithm for color constancy color constancy is the skill by which it is possible to tell the color of an object even under a colored light i interpret the color of an object as its color under a fixed canonical light rather than as a surface reflectance function this leads to an analysis that shows two distinct sets of circumstances under which color constancy is possible in this framework color constancy requires estimating the illuminant under which the image was taken the estimate is then used to choose one of a set of linear maps which is applied to the image to yield a color descriptor at each point this set of maps is computed in advance the illuminant can be estimated using image measurements alone because given a number of weak assumptions detailed in the text the color of the illuminant is constrained by the colors observed in the image this constraint arises from the fact that surfaces can reflect no more light than is cast on them for example if one observes a patch that excites the red receptor strongly the illuminant cannot have been deep blue two algorithms are possible using this constraint corresponding to different assumptions about the world the first algorithm crule will work for any surface reflectance crule corresponds to a form of coefficient rule but obtains the coefficients by using constraints on illuminant color the set of illuminants for which crule will be successful depends strongly on the choice of photoreceptors for narrowband photoreceptors crule will work in an unrestricted world the second algorithm mwext requires that both surface reflectances and illuminants be chosen from finite dimensional spaces but under these restrictive conditions it can recover a large number of parameters in the illuminant and is not an attractive model of human color constancy crule has been tested on real images of mondriaans and works well i show results for crule and for the retinex algorithm of land land 1971 land 1983 land 1985 operating on a number of real images the experimental work shows that for good constancy a color constancy system will need to adjust the gain of the receptors it employs in a fashion analagous to adaptation in humans

critical curve for p q systems of nonlinear wave equations in three space dimensions abstract the existence of the critical curve for p q systems for nonlinear wave equations was already established by d del santo v georgiev and e mitidieri 1997 global existence of the solutions and formation of singularities for a class of hyperbolic systems in geometric optics and related topics f colombini and n lerner eds progress in nonlinear differential equations and their applications vol 32 pp 117 139 birkhauser basel except for the critical case our main purpose is to prove a blow up theorem for which the nonlinearity p q is just on the critical curve in three space dimensions moreover the lower and upper bounds of the lifespan of solutions are precisely estimated including the sub critical case

spreading speeds and periodic traveling waves of a partially sedentary integro difference model this paper is devoted to the study of spatial dynamics of a class of partially sedentary integro difference population models in a periodic habitat for the general case of recruitment functions we establish the existence and computation formula of spreading speeds it is shown that the spreading speed is linearly determinate and coincides with the minimal wave speed of periodic traveling waves some effects of dispersal kernels spatially variations and dispersal probabilities on spreading speeds are also investigated

the strauss conjecture on kerr black hole backgrounds we examine solutions to semilinear wave equations on black hole backgrounds and give a proof of an analog of the strauss conjecture on the schwarzschild and kerr with small angular momentum black hole backgrounds the key estimates are a class of weighted strichartz estimates which are used near infinity where the metrics can be viewed as small perturbations of the minkowski metric and a localized energy estimate on the black hole background which handles the behavior in the remaining compact set

strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation the aim of this article is twofold first we consider the wave equation in the hyperbolic space hi and obtain the counterparts of the strichartz type estimates in this context next we examine the relationship between semilinear hyperbolic equations in the minkowski space and in the hyperbolic space this leads to a simple proof of the recent result of georgiev lindblad and sogge on global existence for solutions to semilinear hyperbolic problems with small data shifting the space time strichartz estimates from the hyperbolic space to the minkowski space yields weighted strichartz estimates in rn x 1r which extend the ones of georgiev lindblad and sogge

spreading speeds and traveling waves for abstract monostable evolution systems abstract this paper is devoted to the development of the theory of spreading speeds and traveling waves for abstract monostable evolution systems with spatial structure under appropriate assumptions we show that the spreading speeds coincide with the minimal wave speeds for monotone traveling waves in the positive and negative directions then we use this theory to study the spatial dynamics of a parabolic equation in a periodic cylinder with the dirichlet boundary condition a reaction diffusion model with a quiescent stage a porous medium equation in a tube and a lattice system in a periodic habitat

blow up of solutions to critical semilinear wave equations with variable coefficients abstract we verify the critical case p p 0 n of strauss conjecture 30 concerning the blow up of solutions to semilinear wave equations with variable coefficients in r n where n 2 the perturbations of laplace operator are assumed to be smooth and decay exponentially fast at infinity we also obtain a sharp lifespan upper bound for solutions with compactly supported data when p p 0 n the unified approach to blow up problems in all dimensions combines several classical ideas in order to generalize and simplify the method of zhou 43 and zhou han 45 exponential eigenfunctions of the laplacian 37 are used to construct the test function q for linear wave equation with variable coefficients and john s method of iterations 13 is augmented with the slicing method of agemi kurokawa and takamura 1 for lower bounds in the critical case

object colour manifold colorimetry can predict which lights will look alike such lights are called metameric two lights are metameric if they have the same tri stimulus values using the tri stimulus values as cartesian coordinates one can represent light colours as points in a 3d space referred to as the colorimetric space all the light colours make a tri dimensional manifold which can be represented as a circular cone in the colorimetric space furthermore colorimetry also claims that reflecting objects illuminated by the same light will look alike as soon as they reflect metameric lights all the object colours are then represented as a closed solid inscribed in the light colour cone provided the illumination is fixed however as argued in this article the reflected light metamerism does not guarantee that the reflecting objects will look identical referred to as colour equivalence especially when there are multiple illuminants moreover colour equivalence cannot be derived from metamerism the colour of a reflecting object under various illuminations is shown to be specified by six numbers referred to as its six stimulus values that can be established by experiment using the six stimulus values one can represent the colours of all the reflecting objects illuminated by various illuminants as a cone without a vertex through a 5d ball