nonexistence of positive solutions to a semilinear elliptic system and blow up estimates for a reaction diffusion system abstract we get simple conditions under which the elliptic system u u p 1 v q 1 v u p 2 v q 2 in r n n 3 with p i q i 1 i 1 2 has no positive radially symmetric solutions then by using this nonexistence result we establish blow up estimates for reaction diffusion system of fujita type u t u u p 1 v q 1 v t v u p 2 v q 2 with the homogeneous dirichlet boundary value condition

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

blowing up of solution for a nonlocal reaction diffusion problem in combustion theory abstract in a nonlocal reaction diffusion model in combustion theory the reaction function involves a physical parameter which is a measure of the strength of the reaction mechanism the purpose of this paper is to show the existence of a critical value such that for a unique global time dependent solution exists and converges to a steady state solution as t and for the solution blows up in finite time a characterization as well as upper and lower bounds of are given

blow up for a degenerate parabolic equation with a nonlocal source abstract in this paper existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution that exists globally or blows up in finite time are obtained for the degenerate parabolic problem x q u t u xx 0 a u m x t d x ku n x t in 0 a 0 t where 0 t a 0 m n 1 k 0 are constants

the blow up rate for a degenerate parabolic equation with a non local source abstract in this paper we establish the local existence of the solution and the finite time blow up result for the equation v v m xx a l l v q dx x l l 0 moreover it is proved that the solution has global blow up and there exist constants c 1 c 2 such that c 1 t 1 1 q 1 max x l l v x c 2 t 1 1 q 1 where t 1 is the blow up time

irrotational or divergence free interpolation this paper deals with interpolation of vectorial data in we build specific vectorial splines which interpolate the data and meet some required vectorial properties we so derive irrotational or divergence free interpolating splines numerical examples compare the so obtained interpolating functions with the ones obtained by independent interpolation on each variable

on global attractor for m laplacian parabolic equation with local and nonlocal nonlinearity abstract in this paper we study the long time behavior of solutions for m laplacian parabolic equation u t m u a x u u f 0 u k y u y t d y g x in 0 with the initial data u x 0 u 0 x l q q 1 and zero boundary condition in two cases for a x a 0 0 and a x 0 are considered we obtain the existence and l p estimate of global attractor a in l p for any p max 1 q the attractor a is in fact a bounded set in w 0 1 m l if a x a 0 0 in and a is bounded in w 0 1 m l p if a x 0 in

new general solutions to linear fredholm integro differential equations and their applications on solving the boundary value problems abstract this paper introduces the n general solution to linear fredholm integro differential equations and sets its properties the conditions for existence of classical general solution and solvability criteria for the equation are provided necessary and sufficient conditions for solvability of linear boundary value problems are established algorithms for construction of the n general solutions are obtained this paper also proposes approximate and numerical methods to solve the boundary value problems

blowup estimates for a semilinear reaction diffusion system this paper deals with the blowup estimates of positive solutions for a semilinear reaction diffusion system ut u u vp vt v uqv with null dirichlet boundary conditions the upper and lower bounds of blowup rates are obtained

forced oscillations of singular dynamical systems with an application to the restricted three body problem abstract we consider forced dynamical systems with two degrees of freedom having singular potentials and we prove existence of infinitely many classical noncollision periodic solutions these solutions have a prescribed rotation behavior with respect to the singularities and a prescribed period the same of the systems they are obtained variationally as minima of a suitable functional on open subsets of a hubert space this investigation was motivated by the elliptic restricted three body problem with arbitrary masses of the two primaries for that problem we obtain infinitely many distinct generalized periodic solutions i e solutions which possibly experience collisions

periodic solutions of a class of singular hamiltonian systems soit r n 0 n n n 3 et soit v c 1 rx r on etudie l existence des solutions periodiques t u t avec une periode prescrite du systeme suivant de n equations differentielles d ordre 2 u v t u

blow up estimate in a reaction diffusion equation with nonlinear nonlocal flux and source abstract this paper deals with a reaction diffusion equation with nonlocal inner source and nonlocal boundary flux besides the influence of exponents we find out that the weighted functions and the measure of the domain could lead to the existence of global solutions for any initial data larger weighted functions require smaller initial data in guaranteeing the existence of global solutions to the problem blow up rates are obtained under different dominations of nonlinearities in one dimensional space the upper and lower bounds of blow up time are determined for all spatial dimensions respectively moreover the solutions blow up only on the boundary when the nonlocal flux dominates the blow up

properties of non simultaneous blow up solutions in nonlocal parabolic equations abstract this paper deals with blow up solutions in parabolic equations coupled via nonlocal nonlinearities subject to homogeneous dirichlet conditions firstly some criteria on non simultaneous and simultaneous blow up are given including four kinds of phenomena i the existence of non simultaneous blow up ii the coexistence of non simultaneous and simultaneous blow up iii any blow up must be simultaneous iv any blow up must be non simultaneous next total versus single point blow up are classified completely moreover blow up rates are obtained for both non simultaneous and simultaneous blow up solutions

a quasilinear reaction diffusion system coupled via nonlocal sources in this paper we establish the critical exponent and the blow up rate for a quasilinear reaction diffusion system with nonlocal nonlinear sources and inner absorptions subject to homogeneous dirichlet conditions and nonnegative initial data it is found that the critical exponent is determined by the interaction among all the six nonlinear exponents from all the three kinds of the nonlinearities while the blow up rate is independent of the nonlinear diffusion exponents due to the effects of the coupled nonlocal sources two kinds of characteristic algebraic systems are introduced to get simple descriptions for the critical exponent and the blow up rate respectively we prove moreover that the blow up could be global due to the nonlocality of the nonlinear sources

full motion and flow field recovery from echo doppler data we present a new computational method for reconstructing a vector velocity field from scattered pulsed wave ultrasound doppler data the main difficulty is that the doppler measurements are incomplete for they do only capture the velocity component along the beam direction we thus propose to combine measurements from different beam directions however this is not yet sufficient to make the problem well posed because 1 the angle between the directions is typically small and 2 the data is noisy and nonuniformly sampled we propose to solve this reconstruction problem in the continuous domain using regularization the reconstruction is formulated as the minimizer of a cost that is a weighted sum of two terms 1 the sum of squared difference between the doppler data and the projected velocities 2 a quadratic regularization functional that imposes some smoothness on the velocity field we express our solution for this minimization problem in a b spline basis obtaining a sparse system of equations that can be solved efficiently using synthetic phantom data we demonstrate the significance of tuning the regularization according to the a priori knowledge about the physical property of the motion next we validate our method using real phantom data for which the ground truth is known we then present reconstruction results obtained from clinical data that originate from 1 blood flow in carotid bifurcation and 2 cardiac wall motion

symmetrical dense optical flow estimation with occlusions detection traditional techniques of dense optical flow estimation do not generally yield symmetrical solutions the results will differ if they are applied between images i 1 and i 2 or between images i 2 and i 1 in this work we present a method to recover a dense optical flow field map from two images while explicitely taking into account the symmetry across the images as well as possible occlusions in the flow field the idea is to consider both displacements vectors from i 1 to i 2 and i 2 to i 1 and to minimise an energy functional that explicitely encodes all those properties this variational problem is then solved using the gradient flow defined by the euler lagrange equations associated to the energy to prove the importance of the concepts of symmetry and occlusions for optical flow computation we have extended a classical approach to handle those experiments clearly show the added value of these properties to improve the accuracy of the computed flows figures appear in color in the online version of this paper

blow up for a degenerate reaction diffusion system with nonlinear nonlocal sources this paper investigates the global existence and blow up of nonnegative solution of the systemu email protected m u p email protected wv q 1dx v email protected n v p email protected wu q 2dx x t email protected 0 t with homogeneous dirichlet boundary conditions where email protected r n is a bounded domain with smooth boundary email protected m n 1 p 1 p 2 q 1 q 2 0 the results depend crucially on the number p i q i m n the domain w and the initial data u 0 x v 0 x moreover we obtain the blow up rate of the blow up solution under some appropriate hypotheses

blow up behavior of positive solutions for a chemical fuel ignition device model blow up behavior of positive solutions of a semi linear parabolic system arising from thermal explosion which subject to the homogenous dirichlet boundary conditions is investigated in particular sufficient conditions for the solutions to blow up are obtained

blow up rate and profile for a degenerate parabolic system coupled via nonlocal sources this paper deals with a degenerate parabolic system with nonlocal nonlinear sources subject to homogeneous dirichlet condition we establish the critical exponent as well as the blow up rate and profile for the system it is interesting to observe that the blow up exponent is determined by the interaction between the nonlinear diffusion and the nonlinear reaction while the blow up rate is independent of the nonlinear diffusion the effects from the nonlocality of the sources are substatial

the utilization of total mass to determine the switching points in the symmetric boundary control problem with a linear reaction term abstract the authors study the problem u t u x x u 0 x 1 t 0 u x 0 0 and u 0 t u 1 t t where t u 0 for t 2 k t t 2 k 1 and t 0 for t 2 k 1 t t 2 k 2 k 0 1 2 with t 0 0 and the sequence t k is determined by the equations 0 1 u x t k d x m for k 1 3 5 and 0 1 u x t k d x m for k 2 4 6 and where 0 m m note that the switching points t k k 1 2 3 are unknown existence and uniqueness are demonstrated theoretical estimates of the t k and t k 1 t k are obtained and numerical verifications of the estimates are presented the case of u x 0 t u x 1 t t is also considered and analyzed

uniform blow up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source in this paper we introduce a new method for investigating the rate and profile of blow up of solutions of diffusion equations with nonlocal nonlinear reaction terms for large classes of equations we prove that the solutions have global blow up and that the rate of blow up is uniform in all compact subsets of the domain this results in a flat blow up profile except for a boundary layer whose thickness vanishes astapproaches the blow up timet in each case the blow up rate of u t is precisely determined furthermore in many cases we derive sharp estimates on the size of the boundary layer and on the asymptotic behavior of the solution in the boundary layer the size of the boundary layer then decays liket t and the solutionu t x behaves like u t d x t tin the boundary layer wheredis the distance to the boundary some fujita type critical exponents results are also given for the cauchy problem

a minimax method for a class of hamiltonian systems with singular potentials abstract this paper presents a minimax method which gives existence and multiplicity results for time periodic solutions of a class of hamiltonian systems when a singular potential is present the singularity satisfies the strong force condition of gordon when milder singularities are permitted a notion of generalized t periodic solution is introduced and we get existence and multiplicity results for such solutions

deformable templates using large deformation kinematics a general automatic approach is presented for accommodating local shape variation when mapping a two dimensional 2 d or three dimensional 3 d template image into alignment with a topologically similar target image local shape variability is accommodated by applying a vector field transformation to the underlying material coordinate system of the template while constraining the transformation to be smooth globally positive definite jacobian smoothness is guaranteed without specifically penalizing large magnitude deformations of small subvolumes by constraining the transformation on the basis of a stokesian limit of the fluid dynamical navier stokes equations this differs fundamentally from quadratic penalty methods such as those based on linearized elasticity or thin plate splines in that stress restraining the motion relaxes over time allowing large magnitude deformations kinematic nonlinearities are inherently necessary to maintain continuity of structures during large magnitude deformations and are included in all results after initial global registration final mappings are obtained by numerically solving a set of nonlinear partial differential equations associated with the constrained optimization problem automatic regridding is performed by propagating templates as the nonlinear transformations evaluated on a finite lattice become singular application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability

the role of non linear diffusion in non simultaneous blow up we study a parabolic system of two non linear reaction diffusion equations completely coupled through source terms and with power like diffusivity under adequate hypotheses on the initial data we prove that non simultaneous blow up is sometimes possible i e one of the components blows up while the other remains bounded the conditions for non simultaneous blow up rely strongly on the diffusivity parameters and significant differences appear between the fast diffusion and the porous medium case surprisingly flat homogeneous in space solutions are not always a good guide to determine whether non simultaneous blow up is possible

left ventricular motion reconstruction based on elastic vector splines in medical imaging it is common to reconstruct dense motion estimates from sparse measurements of that motion using some form of elastic spline thin plate spline snakes and other deformable models etc usually the elastic spline uses only bending energy second order smoothness constraint or stretching energy first order smoothness constraint or a combination of the two these elastic splines belong to a family of elastic vector splines called the laplacian splines this spline family is derived from an energy minimization functional which is composed of multiple order smoothness constraints these splines can be explicitly tuned to vary the smoothness of the solution according to the deformation in the modeled material tissue in this context it is natural to question which members of the family will reconstruct the motion more accurately the authors compare different members of this spline family to assess how well these splines reconstruct human cardiac motion they find that the commonly used splines containing first order and or second order smoothness terms only are not the most accurate for modeling human cardiac motion

wavelet steerability and the higher order riesz transform our main goal in this paper is to set the foundations of a general continuous domain framework for designing steerable reversible signal transformations a k a frames in multiple dimensions d 2 to that end we introduce a self reversible nth order extension of the riesz transform we prove that this generalized transform has the following remarkable properties shift invariance scale invariance inner product preservation and steerability the pleasing consequence is that the transform maps any primary wavelet frame or basis of l 2 bbr d into another steerable wavelet frame while preserving the frame bounds the concept provides a functional counterpart to simoncelli s steerable pyramid whose construction was primarily based on filterbank design the proposed mechanism allows for the specification of wavelets with any order of steerability in any number of dimensions it also yields a perfect reconstruction filterbank algorithm we illustrate the method with the design of a novel family of multidimensional riesz laplace wavelets that essentially behave like the n th order partial derivatives of an isotropic gaussian kernel

constrained restoration and the recovery of discontinuities the linear image restoration problem is to recover an original brightness distribution x sup 0 given the blurred and noisy observations y kx sup 0 b where k and b represent the point spread function and measurement error respectively this problem is typical of ill conditioned inverse problems that frequently arise in low level computer vision a conventional method to stabilize the problem is to introduce a priori constraints on x sup 0 and design a cost functional h x over images x which is a weighted average of the prior constraints regularization term and posterior constraints data term the reconstruction is then the image x which minimizes h a prominent weakness in this approach especially with quadratic type stabilizers is the difficulty in recovering discontinuities the authors therefore examine prior smoothness constraints of a different form which permit the recovery of discontinuities without introducing auxiliary variables for marking the location of jumps and suspending the constraints in their vicinity in this sense discontinuities are addressed implicitly rather than explicitly

a class of non linear non classical parabolic equations abstract in this paper we deal with a class of non classical parabolic equations which arise from some practical problems such as the identification of unknown parameters free boundary problems etc one of the characteristics of this kind of equation is that the maximum principle is no longer valid we will first study the local solvability for a general equation of this kind via an auxiliary problem and the schauder fixed point principle then some a priori estimates are derived to establish the global existence of the solution moreover uniqueness and continuous dependence of the solution are proved finally some examples are given to illustrate the applications of the theory

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

blow up rate estimates for semilinear parabolic systems abstract this paper deals with the blow up rate estimates of positive solutions for semilinear parabolic systems with null dirichlet boundary conditions the upper and lower bounds of blow up rate were obtained

a mathematical analysis of blowup for thermal reactions the spatially nonhomogeneous case the equations describing the induction period process for a super critical high activation energy thermal explosion in a bounded domain are studied a formal proof based on comparison techniques is used to show that the temperature perturbation becomes unbounded as t to t b leqq infty for values of the frank kamenetski parameter delta greater than the critical value upper and lower bound estimates for t b are found by using specified comparison equations a comparison of these bounds with values of t b obtained from numerical solutions of the basic equations shows that the estimates provide an excellent prediction of the escape time when delta is greater than 2 3 times the critical value for smaller values of delta where heat loss is more significant a better comparison equation is required

roles of weight functions in a nonlinear nonlocal parabolic system abstract this paper deals with a semilinear parabolic system with coupled nonlinear nonlocal sources subject to weighted nonlocal dirichlet boundary conditions we establish the conditions for global and non global solutions it is interesting to observe that the weight functions for the nonlocal dirichlet boundary conditions play substantial roles in determining not only whether the solutions are global or non global but also whether for the non global solutions the blowing up occurs for any positive initial data or just for large ones

time weighted blow up profiles in a nonlinear parabolic system with fujita exponent abstract in this paper we deal with a time weighted parabolic system coupled via nonlocal sources firstly we give the critical fujita exponent of solutions secondly we propose the time weighted blow up profiles of solutions thirdly the simultaneous and non simultaneous blow up of solutions are discussed under some conditions on the initial data fourthly besides blow up rates we classify total blow up and single point blow up of solutions at last upper and lower bounds of blow up time are studied according to precise blow up phenomena

majorization minimization algorithms for wavelet based image restoration standard formulations of image signal deconvolution under wavelet based priors regularizers lead to very high dimensional optimization problems involving the following difficulties the non gaussian heavy tailed wavelet priors lead to objective functions which are nonquadratic usually nondifferentiable and sometimes even nonconvex the presence of the convolution operator destroys the separability which underlies the simplicity of wavelet based denoising this paper presents a unified view of several recently proposed algorithms for handling this class of optimization problems placing them in a common majorization minimization mm framework one of the classes of algorithms considered when using quadratic bounds on nondifferentiable log priors shares the infamous singularity issue si of iteratively re weighted least squares irls algorithms the possibility of having to handle infinite weights which may cause both numerical and convergence issues in this paper we prove several new results which strongly support the claim that the si does not compromise the usefulness of this class of algorithms exploiting the unified mm perspective we introduce a new algorithm resulting from using bounds for nonconvex regularizers the experiments confirm the superior performance of this method when compared to the one based on quadratic majorization finally an experimental comparison of the several algorithms reveals their relative merits for different standard types of scenarios

monte carlo sure a black box optimization of regularization parameters for general denoising algorithms we consider the problem of optimizing the parameters of a given denoising algorithm for restoration of a signal corrupted by white gaussian noise to achieve this we propose to minimize stein s unbiased risk estimate sure which provides a means of assessing the true mean squared error mse purely from the measured data without need for any knowledge about the noise free signal specifically we present a novel monte carlo technique which enables the user to calculate sure for an arbitrary denoising algorithm characterized by some specific parameter setting our method is a black box approach which solely uses the response of the denoising operator to additional input noise and does not ask for any information about its functional form this therefore permits the use of sure for optimization of a wide variety of denoising algorithms we justify our claims by presenting experimental results for sure based optimization of a series of popular image denoising algorithms such as total variation denoising wavelet soft thresholding and wiener filtering smoothing splines in the process we also compare the performance of these methods we demonstrate numerically that sure computed using the new approach accurately predicts the true mse for all the considered algorithms we also show that sure uncovers the optimal values of the parameters in all cases

global existence and blow up for a nonlinear reaction diffusion system abstract we consider the nonlinear reaction diffusion system u t u u m 1 v n 1 v t v u m 2 v n 2 subject to dirichlet boundary conditions andm2 m1 1 n1 n2 1 we prove that ifm1 1 n2 1 andm2n1 1 m1 1 n2 all nonnegative solutions are global while ifm1 1 orn2 1 orm2n1 1 m1 1 n2 both global existence and finite time blow up coexist

on regularized reconstruction of vector fields in this paper we give a general characterization of regularization functionals for vector field reconstruction based on the requirement that the said functionals satisfy certain geometric invariance properties with respect to transformations of the coordinate system in preparation for our general result we also address some commonalities of invariant regularization in scalar and vector settings and give a complete account of invariant regularization for scalar fields before focusing on their main points of difference which lead to a distinct class of regularization operators in the vector case finally as an illustration of potential we formulate and compare quadratic l2 and total variation type l1 regularized denoising of vector fields in the proposed framework

asymptotic behaviour of nonlocal reaction diffusion equations abstract the existence of a global attractor in l 2 is established for a reaction diffusion equation on a bounded domain in r d with dirichlet boundary conditions where the reaction term contains an operator f l 2 l 2 which is nonlocal and possibly nonlinear existence of weak solutions is established but uniqueness is not required compactness of the multivalued flow is obtained via estimates obtained from limits of galerkin approximations in contrast with the usual situation these limits apply for all and not just for almost all time instants