on approximate solutions to the wavefront speed problem we propose an approximate method to obtain the speed of wavefronts it is built up from a known variational principle for a range of systems of biological and physical interest comparison to previously known solutions and to numerical simulations shows the powerfulness of our approximate technique for time delayed equations we also propose an alternative approximate solution based on the renormalization group approach and we compare both approximations

exact and approximate solutions of the perspective three point problem model based pose estimation techniques that match image and model triangles require large numbers of matching operations in real world applications the authors show that by using approximations to perspective 2d lookup tables can be built for each of the triangles of the models an approximation called weak perspective has been applied previously to this problem the authors consider two other perspective approximations paraperspective and orthoperspective these approximations produce lower errors for off center image features than weak perspective

the speed of reaction diffusion wavefronts in nonsteady media the evolution of the speed of wavefronts for reaction diffusion equations with time varying parameters is analysed we make use of singular perturbative analysis to study the temporal evolution of the speed for pushed fronts the analogy with hamilton jacobi dynamics allows us to consider the problem for pulled fronts which is described by kolmogorov petrovskii piskunov kpp reaction kinetics both analytical studies are in good agreement with the results of numerical solutions

linear and nonlinear marginal stability for fronts of hyperbolic reaction diffusion equations we study traveling fronts of equations of the form u mathrm tt ensuremath varphi u u x u mathrm xx f u a criterion for the transition from linear to nonlinear marginal stability is established for positive functions ensuremath varphi u and for any reaction term f u for which the usual parabolic reaction diffusion equation u t u mathrm xx f u admits a front as an application we treat reaction diffusion systems with transport memory

transition from pushed to pulled fronts in piecewise linear reaction diffusion systems abstract the front dynamics in reaction diffusion equations with a piecewise linear reaction term is studied a transition from pushed to pulled fronts when they propagate into the unstable state is found using a variational principle this transition occurs for a critical value of the discontinuity position in the reaction function in particular we study how the transition depends on the properties of the reaction term and on the delay time our results are in good agreement with the numerical solutions of the model

pattern propagation in nonlinear dissipative systems abstract we discuss the problem of pattern selection in situations where a stable nonuniform state of a nonlinear dissipative system propagates into an initially unstable homogeneous region our strategy is to consider this process as a generalization of front propagation in a nonlinear diffusion problem for which rigorous results are known and we point out that these known properties are consistent with a marginal stability hypothesis that has been suggested in the theory of dendritic crystal growth we then describe a more general interpretation of the marginal stability hypothesis and finally present numerical evidence for its validity from three different pattern forming models

wavefronts in bistable hyperbolic reaction diffusion systems abstract we study the dynamics of wavefronts that arise in bistable systems with correlated diffusion in time for the piecewise linear reaction term the speed of propagation of these fronts is obtained analytically the shape and the width of the front are analyzed by means of two different methods usually employed for parabolic diffusion it is shown that for hyperbolic reaction diffusion equations the wavefront presents a discontinuity in the slope

the existence of infinitely many solutions of a class of nonlinear elliptic equations with neumann boundary condition for both resonance and oscillation problems abstract in this paper we study and discuss nonlinear elliptic equations with neumann boundary condition for both resonance and oscillation problem and obtain new results on the exactly infinitely many positive and negative solutions which are all nonconstant the study of problem 1 1 are based on the variational methods and critical point theory we prove the conclusion by using sub sup solution method mountain pass theorem in order intervals leray schauder degree theory and more theory

global analysis of pattern selection and bifurcations in monostable reaction diffusion systems we study a piecewise linear version of a one component monostable reaction diffusion model in a bounded domain subjected to partially reflecting boundary conditions albedo b c we analyze the local and the global stability of the merging patterns and detect a bifurcation of the uniform solution induced by changes in the reflectivity of the boundaries

shift in the speed of reaction diffusion equation with a cut off pushed and bistable fronts abstract we study the change in the speed of pushed and bistable fronts of the reaction diffusion equation in the presence of a small cut off we give explicit formulas for the shift in the speed for arbitrary reaction terms f u the dependence of the speed shift on the cut off parameter is a function of the front speed and profile in the absence of the cut off in order to determine the speed shift we solve the leading order approximation to the front profile u z in the neighborhood of the leading edge and use a variational principle for the speed we apply the general formula to the nagumo equation and recover the results which have been obtained recently by geometric analysis the formulas given are of general validity and we also apply them to a class of reaction terms which have not been considered elsewhere

speed of fronts of generalized reaction diffusion equations different problems may be described in terms of the reaction diffusion equation u t 5u xx 1f u where f is a nonlinear term with at least two equilibrium points it has been established rigorously 1 that sufficiently localized initial conditions evolve asymptotically into a traveling monotonic wave front u x2ct joining two equilibrium states for simplicity we will consider reaction terms f 0 which vanish at u50 and at u51 there is a wide class of reaction terms f u for which this asymptotic speed is given by 2 the kolmogorv petrovskii piskunov kpp value c kpp 5 2 a f8 0 this is the minimal value of the speed that follows from a linear analysis at the equilibrium points the extension of this behavior to pattern forming systems is called the 3 marginal stability hypothesis for other reaction terms this linear or c kpp value represents a lower bound to the speed there exist local 4 and global 5 6 variational principles that enable one to determine the speed for arbitrary reaction terms f u as well as methods based on approximate solutions of the differential equation itself 7 8 while all the above results have been established rigorously other problems are described by other types of reactiondiffusion equations in which nonlinearities may appear on derivative terms generalized diffusion equations of the form ut5uxx1f ux u and the stability of its traveling fronts have been studied 9 10 while the stability of its traveling waves has been established the problem of determining which of the possible traveling waves will be the asymptotic state has not been clarified in general in recent work 11 one such type of generalized reaction diffusion equation namely

wavefront solutions of a nonlinear telegraph equation abstract the paper is concerned with a class of nonlinear second order hyperbolic partial differential equations necessary and sufficient conditions for the occurrence of traveling wave solutions are derived and the spectra of wave speeds for which such solutions exist are characterized an integral equation approach is employed models of branching random walks conduction in transmission lines and biological dispersal provide illustrations

inverse solution for some travelling wave reaction diffusion problems the authors obtain a novel infinite parametric class of exact stable travelling wave solutions of the one component one dimensional reaction diffusion equation by means of an inverse method a number of explicit examples are worked out in terms of elementary functions some special cases of two component travelling wave reaction diffusion problems can be reduced to the one component case and thus solved by this method

multiple solutions and sign changing solutions of a class of nonlinear elliptic equations with neumann boundary condition in this paper we study and discuss nonlinear elliptic equations with neumann boundary condition for oscillation problem we obtain infinitely many positive and negative solutions of 1 1 which are all nonconstant and get at least two nonconstant solutions in every order interval under resonance case moreover we yield infinitely many sign changing solutions of 1 1 under some assumptions furthermore we give a precise description of critical groups of some kinds of critical points we draw the conclusions by using sub sup solution method mountain pass theorem in order intervals leray schauder degree theory and morse theory

multiple solutions for semilinear elliptic boundary value problems with double resonance abstract in this paper we study the multiplicity of nontrivial solutions of semilinear elliptic boundary value problems which may be double resonance near infinity between two consecutive eigenvalues of with zero dirichlet boundary data the methods we use here are morse theory minimax methods and bifurcation theory

progressive match expansion via coherent subspace constraint in this paper a quasi dense matching algorithm called progressive match expansion via coherent subspace pecs is proposed our algorithm starts from a set of sparse seeds and iteratively expands potential matches in the region around the seeds until no more matches could be found the main difference from previous methods is that our method computes a coherent non rigid transformation to relate the matching pixels instead of using local planar affine model to approximate the real scene surface within the expanding region the points in the expanding region are treated as a whole and all the matches satisfying the transformation are found at once first dense sift descriptors are extracted and a subspace encoding the feature similarity between two point sets is computed this embedding pulls two points closer if they have similar features and makes the non rigid transformation learning more robust second a coherent non rigid transformation in the subspace is computed to move one point set towards the other and the spatially aligned two points denote a match the proposed model is robust to scenes with non smooth surface and experiment results reveal the good performance in both 2d image matching and 3d reconstruction

on the influence of reflective boundary conditions on the statistics of poisson kac diffusion processes abstract we analyze the influence of reflective boundary conditions on the statistics of poisson kac diffusion processes and specifically how they modify the poissonian switching time statistics after addressing simple cases such as diffusion in a channel and the switching statistics in the presence of a polarization potential we thoroughly study poisson kac diffusion in fractal domains diffusion in fractal spaces highlights neatly how the modification in the switching time statistics associated with reflections against a complex and fractal boundary induces new emergent features of poisson kac diffusion leading to a transition from a regular behavior at shorter timescales to emerging anomalous diffusion properties controlled by walk dimensionality of the fractal set

speed of reaction diffusion fronts in spatially heterogeneous media the front speed problem for nonuniform reaction rate and diffusion coefficient is studied by using singular perturbation analysis the geometric approach of hamilton jacobi dynamics and the local speed approach exact and perturbed expressions for the front speed are obtained in the limit of large times for linear and fractal heterogeneities the analytic results have been compared with numerical results exhibiting a good agreement finally we reach a general expression for the speed of the front in the case of smooth and weak heterogeneities

on the existence of multiple ordered solutions of nonlinear eigenvalue problems on etudie le probleme de dirichlet u f u dans u o sur ou est un domaine borne lisse de r n n 1 la fonction a valeur reelle f o r est supposee c 1 et o est un parametre reel on etudie le lien entre les changements de signe de la fonction f et l existence de plusieurs solutions positives ordonnees

global stability of stationary patterns in bistable reaction diffusion systems we study a piecewise linear version of a one component one dimensional reaction diffusion bistable model with the aim of analyzing the effect of boundary conditions on the formation and stability of stationary patterns the analysis proceeds through the study of the behavior of the lyapunov functional in terms of a control parameter the reflectivity at the boundary we show that in this example this functional has a very simple and direct geometrical interpretation

travelling kinks in schlogl s second model for non equilibrium phase transitions using the separation technique developed by osborne and stuart 1980 travelling wave solutions are written down for the nonlinear reaction diffusion equation of schlogl s second model assuming that the necessary conditions for the static phase coexistence are satisfied

pattern forming pulled fronts bounds and universal convergence we analyze the dynamics of pattern forming fronts which propagate into an unstable state and whose dynamics is of the pulled type so that their asymptotic speed is equal to the linear spreading speed v we discuss a method that allows to derive bounds on the front velocity and which hence can be used to prove for among others the swift hohenberg equation the extended fisher kolmogorov equation and the cubic complex ginzburg landau equation that the dynamically relevant fronts are of the pulled type in addition we generalize the derivation of the universal power law convergence of the dynamics of uniformly translating pulled fronts to both coherent and incoherent pattern forming fronts the analysis is based on a matching analysis of the dynamics in the leading edge of the front to the behavior imposed by the nonlinear region behind it numerical simulations of fronts in the swift hohenberg equation are in full accord with our analytical predictions

traveling waves in a reaction diffusion system diffusion with finite velocity and kolmogorov petrovskii piskunov kinetics an asymptotic method is presented for the analysis of the traveling waves in the one dimensional reaction diffusion system with the diffusion with a finite velocity and kolmogorov petrovskii piskunov kinetics the analysis makes use of the path integral approach scaling procedure and the singular perturbation techniques involving the large deviations theory for the poisson random walk the exact formula for the position and speed of reaction front is derived it is found that the reaction front dynamics is formally associated with the relativistic hamiltonian lagrangian mechanics

multiple solutions for semilinear elliptic equations with neumann boundary condition and jumping nonlinearities abstract we obtain nonconstant solutions of semilinear elliptic neumann boundary value problems with jumping nonlinearities when the asymptotic limits of the nonlinearity fall in the type i l l 2 and ii l l 1 regions formed by the curves of the fucik spectrum furthermore we have at least two nonconstant solutions in every order interval under resonance case in this paper we apply the sub sup solution method fucik spectrum mountain pass theorem in order intervals degree theory and morse theory to get the conclusions

determination of the attitude of 3d objects from a single perspective view a method for finding analytical solutions to the problem of determining the attitude of a 3d object in space from a single perspective image is presented its principle is based on the interpretation of a triplet of any image lines as the perspective projection of a triplet of linear ridges of the object model and on the search for the model attitude consistent with these projections the geometrical transformations to be applied to the model to bring it into the corresponding location are obtained by the resolution of an eight degree equation in the general case using simple logical rules it is shown on examples related to polyhedra that this approach leads to results useful for both location and recognition of 3d objects because few admissible hypotheses are retained from the interpolation of the three line segments line matching by the prediction verification procedure is thus less complex

variational principles and the shift in the front speed due to a cutoff we apply variational principles to reaction diffusion equations in order to predict for a general reaction term the sign of the shift in the front speed due to a cutoff we develop an improved variational principle to obtain the shift in the front speed for a wide range of reaction terms and the theoretical results so obtained are in excellent agreement with numerical solutions this work proves that variational principles are an optimal framework to deal with fronts propagating into unstable and metastable states under cutoff

effects of transport memory and nonlinear damping in a generalized fisher s equation memory effects in transport require for their incorporation into reaction diffusion investigations a generalization of traditional equations the well known fisher s equation which combines diffusion with a logistic nonlinearity is generalized to include memory effects and traveling wave solutions of the equation are found comparison is made with alternative generalization procedures

nontrivial solutions for elliptic resonant problems abstract nontrivial solutions for elliptic resonant problems are obtained via morse theory to compute the critical groups at infinity of the relevant functional we propose a new approach by combining the homotopy and reduction methods and the alexander duality theorem

renormalization group theory and variational calculations for propagating fronts we study the propagation of uniformly translating fronts into a linearly unstable state both analytically and numerically we introduce a perturbative renormalization group rg approach to compute the change in the propagation speed when the fronts are perturbed by structural modification of their governing equations this approach is successful when the fronts are structurally stable and allows us to select uniquely the numerical experimentally observable propagation speed for convenience and completeness the structural stability argument is also briefly described we point out that the solvability condition widely used in studying dynamics of nonequilibrium systems is equivalent to the assumption of physical renormalizability we also implement a variational principle due to hadeler and rothe which provides a very good upper bound and in some cases even exact results on the propagation speeds and which identifies the transition from linear to nonlinear marginal stability as parameters in the governing equation are varied

an electrothermal instability the influence of albedo boundary conditions on the stationary states of an exactly solvable model abstract in order to study the effect of partially reflective albedo boundary conditions on pattern formation and stability in reaction diffusion systems we have analyzed an exactly soluble model of an electrothermal instability the ballast resistor the present results allow a continuous interpolation between the results corresponding to neumann and dirichlet boundary conditions and they allow qualitative changes in the patterns to be followed

higher dimensional localized patterns in excitable media abstract the excitable reaction diffusion equation model of the form e u t e 2 2 u u v v t 2 v u v is considered when u is assumed to be of mckean s piecewise linear type the interfacial approach can be applied to the stability of various localized patterns in higher dimensional spaces it is shown that a band shaped localized pattern is destabilized into a zig zag mode or a varicose mode and that a disk shaped localized pattern is destabilized into static modes and when is small into an oscillatory mode like a breather motion numerical simulations are performed to confirm such destabilizations for more general nonlinear functions u

reaction diffusion wave fronts multigeneration biological species under climate change a generalization of reaction diffusion models to multigeneration biological species is presented it is based on more complex random walks than those in previous approaches the new model is developed analytically up to infinite order our predictions for the speed agree to experimental data for several butterfly species better than existing models the predicted dependence for the speed on the number of generations per year allows us to explain the change in speed observed for a specific invasion

numerical methods for nonlinear second order hyperbolic partial differential equations i time linearized finite difference methods for 1 d problems abstract a three parameter family of finite difference methods for one dimensional hyperbolic equations with damping and nonlinearities based on the introduction of a new dependent variable and three implicitness parameters for the time discretization and the diffusion and reaction terms is presented and shown to result in two time level semi discrete equations second order accurate spatial discretizations and time linearization of the nonlinear source terms are shown to result in three time level linear finite difference equations which are second order accurate in time whenever the reaction and diffusion terms are allocated in the proportion 1 2 1 to the past current and future time levels second order accurate in time time linearized three point compact operator methods for the spatial derivatives which only involve three time levels and three grid points and are fourth order accurate in space are also presented and their linear stability analyzed an exhaustive comparison between analytical and numerical results indicates that the accuracy of time linearized methods increases as the time step and grid spacing are decreased and is nearly independent of the order of the spatial discretization when there is a sufficient number of grid points to resolve the wave structure and the best accuracy is achieved when the three implicitness parameters are equal to 1 2 it is also shown that the accuracy of time linearized methods is a strong function of the wave speed as the wave speed is increased and the wave equation tends to a parabolic one the methods are still three time level techniques which may not preserve the positivity of the solution whereas a crank nicolson discretization of the corresponding parabolic equation does preserve this property provided that there are no mathematical incompatibilities between the initial and the boundary conditions it is also shown that for one dimensional wave equations with monotonic kinetics and time dependent forcing there are very few differences between second and first order time accurate discretizations of the diffusion terms provided that the time step and grid size are sufficiently small and the discretization of the reaction terms plays a less important rule than that of the diffusion terms

fronts from integrodifference equations and persistence effects on the neolithic transition we extend a previous model of the neolithic transition in europe j fort and v mendez phys rev lett 82 867 1999 by taking two effects into account i we do not use the diffusion approximation which corresponds to second order taylor expansions and ii we take proper care of the fact that parents do not migrate away from their children we refer to this as a time order effect in the sense that it implies that children grow up with their parents before they become adults and can survive and migrate we also derive a time ordered second order equation which we call the sequential reaction diffusion equation and use it to show that effect ii is the most important one and that both of them should in general be taken into account to derive accurate results as an example we consider the neolithic transition the model predictions agree with the observed front speed and the corrections relative to previous models are important up to 70

motion from point matches multiple of solutions in this paper we study the multiplicity of solutions of the motion problem given n point matches between two frames how many solutions are there to the motion problem we show that the maximum number of solutions is 10 when 5 point matches are available this settles a question that has been around in the computer vision community for a while we follow two tracks we show that the two approaches are compatible and yield the same result we then describe a computer implementation of the second approach that uses maple a language for symbolic computation the program allows us to compute exactly the solutions for any configuration of 5 points some experiments are described

effect of initial conditions on the speed of reaction diffusion fronts the effect of initial conditions on the speed of propagating fronts in reaction diffusion equations is examined in the framework of the hamilton jacobi theory we study the transition between quenched and nonquenched fronts both analytically and numerically for parabolic and hyperbolic reaction diffusion nonhomogeneous media are also analyzed and the effect of algebraic initial conditions is also discussed

speed of wave front solutions to hyperbolic reaction diffusion equations the asymptotic speed problem of front solutions to hyperbolic reaction diffusion hrd equations is studied in detail we perform linear and variational analyses to obtain bounds for the speed in contrast to what has been done in previous work here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds for some functions it is possible to determine the speed without any uncertainty this is also achieved for some systems of hrd i e time delayed lotka volterra equations that take into account the interaction among different species an analytical analysis is performed for several systems of biological interest and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently s1063 651x 99 06211 x

on the time dependent cattaneo law in space dimension one we consider the one dimensional wave equation e u tt u xx 1 e f u u t f u h where e e t is a decreasing function vanishing at infinity providing a model for heat conduction of cattaneo type with thermal resistance decreasing in time within the theory of processes on time dependent spaces we prove the existence of an invariant time dependent attractor which converges in a suitable sense to the attractor of the classical fourier equation u t u xx f u h formally arising in the limit t

recursive depth parametrization of monocular visual navigation observability analysis and performance evaluation abstract in this paper the theoretical and practical feasibility of estimating ego motion in monocular navigation is under investigation in particular this paper concerns the observability issues of monocular navigation models in order to recover the ego motion of the monocular camera from 2d two dimension image sequence this paper proposes a novel recursive parametric model this model differs from other traditional parametric models with the reduced state dimension and the consistent observability of system state in addition the consistent observability of different models are compared by using time varying observability analysis theory at the end of this paper two groups of experiments are implemented to validate the effectiveness of the proposed method

multiplicity results and qualitative properties for neumann semilinear elliptic problems abstract in this paper we establish the existence of multiple ordered classical solutions for neumann semilinear elliptic problems and provide qualitative information about them no symmetry assumptions are required neither on the nonlinearity nor on the domain for some results the growth of the nonlinearity at infinity is arbitrary we also consider the cases when the nonlinearity is either superlinear or asymptotically linear with strong resonances extensive use is made of the mountain pass theorem and leray schauder topological degree

multiplicity results for semilinear elliptic problems at resonance and with jumping nonlinearities abstract in the present paper we develop a method to deal with multiple existence of solutions of nonlinear elliptic problems and give some multiple existence results for elliptic boundary value problems at resonance and problems with jumping nonlinearities

on theory of pulse transmission in a nerve fibre the ray method is used to analyse pulse propagation in a nerve fibre the initial equations are considered to be hyperbolic i e with a finite velocity of propagation and the corresponding evolution equation is obtained the evolution equation that describes the dynamical side of the process is an equation of the first order being the natural result of applying the ray method this approach avoids the paradox of infinite velocity arising from the initial parabolic system used in the hodgkin huxley model but does not make the final governing equation more complicated the biochemical side of the process is described by means of the hodgkin huxley or fitzhugh nagumo models the steady state solution if it exists leads to an equation of the lienard type and the correspondence between the equations of the catastrophe theory and the usual nerve pulse equations is established

multiple interpretations of a pair of images of a surface it is known that if two optical images of a visually textured surface projected from finitely separated viewpoints allow more than one 3d interpretation then the surface must be part of a quadric passing through the two viewpoints it is here shown that this quadric is either a plane or a ruled surface of a type first considered by maybank in a study of ambiguous optic flow fields and that in the latter case three is the maximum number of distinct interpretations that the two images can sustain

different microscopic interpretations of the reaction telegrapher equation in this paper we provide some new insights into the microscopic interpretation of the telegrapher s and the reaction telegrapher equations we use the framework of continuous time random walks to derive the telegrapher s equation from two different perspectives reported before the kinetic derivation kd and the delayed random walk derivation drwd we analyze the similarities and the differences between both derivations paying special attention to the case when a reaction process is also present in the system as a result we are able to show that the equivalence between the kd and the drwd can break down when transport and reaction are coupled processes also this analysis allows us to elaborate on the specific role of relaxation effects in reaction diffusion processes

pattern formation in malthusian growth with transport memory we consider the effect of memory dependent transport on the survivability of a population dispersing in a closed domain surrounded by a hostile environment the model we use combines memory dependent diffusion with malthusian growth the former introduces an additional parameter the correlation time for memory effects that must be taken into account in determining the critical length below which survival does not occur results are obtained for all possible parametric conditions and the relevance to non linear growth conditions is discussed

on a nonlinear hyperbolic equation with a bistable reaction term abstract nonlinear second order hyperbolic equations are gaining ground as models in many areas of application as extensions of parabolic reaction diffusion equations that might otherwise be used the theory of travelling wave solutions of such reaction diffusion equations is well established the present paper is concerned with its counterpart for the wider class of equations in the particular case that the reaction term is bistable conditions that are necessary and sufficient for the existence and uniqueness of these solutions are determined a combination of traditional ordinary differential equation techniques and an innovatory integral equation approach is employed

dynamical features of reaction diffusion fronts in fractals the speed of front propagation in fractals is studied by using i the reduction of the reaction transport equation into a hamilton jacobi equation and ii the local equilibrium approach different equations proposed for describing transport in fractal media together with logistic reaction kinetics are considered finally we analyze the main features of wave fronts resulting from this dynamic process i e why they are accelerated and what is the exact form of this acceleration

variational characterization of the speed of propagation of fronts for the nonlinear diffusion equation we give an integral variational characterization for the speed of fronts of the nonlinear diffusion equationut uxx f u withf 0 f 1 0 andf 0 in 0 1 which permits in principle the calculation of the exact speed for arbitraryf