cauchy problems of semilinear pseudo parabolic equations abstract this paper concerns with the cauchy problems of semilinear pseudo parabolic equations after establishing the necessary existence uniqueness and comparison principle for mild solutions which are also classical ones provided that the initial data are appropriately smooth we investigate large time behavior of solutions it is shown that there still exist the critical global existence exponent and the critical fujita exponent for pseudo parabolic equations and that these two critical exponents are consistent with the corresponding semilinear heat equations

critical blowup and global existence numbers for a weakly coupled system of reaction diffusion equations let d rn be either all of rn or else a cone in rn whose vertex we may take to be at the origin without loss of generality let pi qj i 1 2 be nonnegative with 0 p1 q1 p2 q2 we consider the long time behavior of nonnegative solutions of the system u t delta u u p 1 v q 1 v t delta v u p 2 v q 2 s in d 0 with u0 v0 0 on d u v t x 0 0 0 t x u0 0 0 u0 0 e l d we obtain fujita type global existence global nonexistence theorems for s analogous to the classical result of fujita and others for the initial value problem for ut u up u x 0 u0 x 0 the principal result in the case d rn and p2q1 0 is that when p1 1 the system behaves like the single equation ut u up1vq1 with respect to fujita type blowup theorems whereas if p1 1 the behavior of the system is more complicated some of the results extend those of escobedo herrero when d rn and of levine when d is a cone these authors considered s in the case of p1 q2 0 an example of nonuniqueness is also given

piecewise linear mapping functions for image registration abstract a new approach to determination of mapping functions for registration of digital images is presented given the coordinates of corresponding control points in two images of the same scene first the images are divided into triangular regions by triangulating the control points then a linear mapping function is obtained by registering each pair of corresponding triangular regions in the images the overall mapping function is then obtained by piecing together the linear mapping functions

fujita type exponent for fully nonlinear parabolic equations and existence results abstract in this paper we prove that a class of parabolic equations involving a second order fully nonlinear uniformly elliptic operator has a fujita type exponent these exponents are related with an eigenvalue problem in all r n and play the same role in blow up theorems as the classical p 1 2 n introduced by fujita for the laplacian we also obtain some associated existence results

nonexistence of global solutions of a nonlinear hyperbolic system consider the initial value problem utt au ivip vtt av u q x e r t t o u x 0 f x v x 0 h x ut x 0 g x vt x 0 x with 1 0 we show that there exists a bound b n oo such that if 1 pq b n all nontrivial solutions with compact support blow up in finite time

global existence and nonexistence for degenerate parabolic equations with nonlinear boundary flux in this paper by constructing various kinds of sub and super solutions and using the basic properties of m matrix we give the necessary and sufficient conditions of global existence for nonnegative solutions to a degenerate parabolic system with completely coupled boundary conditions which generalize the recent results of for instance cui z cui critical curves of the non newtonian polytropic filtration equations coupled with nonlinear boundary conditions nonlinear anal 68 2008 3201 3208 zhou mu j zhou c mu algebraic criteria for global existence or blow up for a boundary coupled system of nonlinear diffusion equations appl anal 86 2007 1185 1197 etc

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

the role of critical exponents in blow up theorems the sequel abstract in 27 fujita showed that for positive solutions the initial value problem in r n for u t u u p with p 1 exhibited the following behavior if p p c 1 2 n then the initial value problem does not have any nontrivial non negative solution existing on r n 0 a global solution whereas if p p c there exist global small data positive solutions as well as solutions which are non global we call such a result a blow up theorem of fujita type in 50 levine discussed the various theorems of this type that had appeared in the literature prior to 1990 in this paper we revisit the literature since 1990

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

an equation whose fujita critical exponent is not given by scaling in this paper we prove sharp blow up and global existence results for a heat equation with nonlinear memory it turns out that the fujita critical exponent is not the one which would be predicted from the scaling properties of the equation

numerical methods for determining the stability and response of periodic systems with applications to helicopter rotor dynamics and aeroelasticity abstract this paper reviews and extends some recently developed numerical techniques for analyzing the stability linear response and nonlinear response of periodic systems which are governed by ordinary differential equations with periodic coefficients the main emphasis is on applications aimed at rotor blade aeroelastic stability and response calculations in forward flight first floquer theory is br4iefly reviewed and numerically efficient methods for evaluating the transition matrix at the end of one period are described next the numerical treatment of the linear response problem is discussed finally the numerical solution of the nonlinear response problem is treated using quasilinearization and periodic shooting applications illustrating numerical properties of the methods are described

continuation of blowup solutions of nonlinear heat equations in several space dimensions the possible continuation of solutions of the nonlinear heat equation in r n r ut u m u p with m 0 p 1 after the blowup time is studied and the different continuation modes are discussed in terms of the exponents m and p thus for m p 2 we find a phenomenon of nontrivial continuation where the regionfx u x t 1g is bounded and propagates with finite speed this we call incomplete blowup for n 3 and p m n 2 n 2 we find solutions that blow up at finite t t and then become bounded again for t t otherwise we find that blowup is complete for a wide class of initial data in the analysis of the behavior for large p a list of critical exponents appears whose role is described we also discuss a number of related problems and equations we apply the same technique of analysis to the problem of continuation after the onset of extinction for example for the equation ut u m u p m 0

critical exponents for the blowup of solutions with sign changes in a semilinear parabolic equation ii abstract the blowup of solutions of the cauchy problem formula is studied let k be the set of functions on r which change sign k times it is shown that for p k 1 2 k 1 k 0 1 2 any solution with u 0 k blows up in finite time if 1 p p k whereas a global solution with u 0 k exists if p p k this is an extension of our previous result 17 in which a fast decay condition was imposed on initial data it is also shown in this paper that if u0 decays more slowly than x 2 p 1 as x then the solution blows up in finite time regardless of the number of sign changes

large time behavior for convection diffusion equations in rn abstract we describe the large time behavior of solutions of the convection diffusion equation u t u a u q 1 u in 0 r n with a r n and q 1 1 n n 1 when q 1 1 n we prove that the large time behavior of solutions with initial data in l 1 r n is given by a uniparametric family of self similar solutions the relevant parameter is the mass of the solution that is conserved for all t our result extends to dimensions n 1 well known results on the large time behavior of solutions for viscous burgers equations in one space dimension the proof is based on la salle s invariance principle applied to the equation written in its self similarity variables when q 1 1 n the convection term is too weak and the large time behavior is given by the heat kernel in this case the result is easily proved applying standard estimates of the heat kernel on the integral equation related to the problem

blow up and global existence of solutions to an inhomogeneous parabolic system abstract we study the critical phenomenon of a weakly coupled inhomogeneous parabolic system which is largely unexplored even though the homogeneous problem has been widely studied the conditions on the powers of the nonlinear terms are new compared with the well known homogeneous case the method appears to be different from the standard ones in the literature an application to the lame emden system is also given

on critical exponents for the heat equation with a mixed nonlinear dirichlet neumann boundary condition abstract in this paper we consider the heat equationut uin an unbounded domain rnwith a partly dirichlet conditionu x t 0 and a partly neumann conditionu upon the boundary wherep 1 and is the exterior unit normal on the boundary it is shown that for a sectorial domain inr2and anorthantdomain inrnthere exists an explicit critical exponentpc 1 such that all positive solutions blow up in finite time whenp 1 pc while there exist positive global solutions ifp pcand initial data are suitably small all our blowup results include the critical case

global and blow up solutions for nonlinear parabolic equations with robin boundary conditions abstract in this paper we discuss the blow up for classical solutions to the following class of parabolic equations with robin boundary condition b u t g u u f u in 0 t u n u 0 on 0 t u x 0 h x 0 in where is a bounded domain of r n n 2 with smooth boundary by constructing some appropriate auxiliary functions and using a first order differential inequality technique we derive conditions on the data which guarantee the blow up or the global existence of the solution for the blow up solution a lower bound on blow up time is also obtained moreover some examples are presented to illustrate the applications

global existence and blow up of solutions to a class of doubly degenerate parabolic equations coupled via nonlinear boundary flux the paper deals with the critical curve for a degenerate parabolic system coupled via nonlinear boundary flux by constructing the self similar super solution and subsolution we obtain the critical global existence curve and the critical curve of fujita type is conjectured with the aid of some new results an interesting feature of our results is that the critical global existence curve and the critical fujita curve are determined by a matrix and by the solution of a linear algebraic system respectively

existence and nonexistence of global solutions forut δu a x upinrd abstract we study nonnegative solutions of the equation u t 2 u a x u p in r d t 0 under the assumption that a x 0 is on the order x m for m 2 or that 0 a x c x 2 extending the classical result of fujita and more recent results of bandle and levine and of levine and meier we find a critical exponent p p m d such that if 1 p p then there exist no solutions that are global in time while if p p then there exist both global and nonglobal solutions

a note on semilinear heat equation in hyperbolic space abstract bandle et al 1 obtained a quite interesting result about a semilinear heat equation that the fujita exponent relative to the whole hyperbolic space is just the same as that relative to bounded domain in euclidean space and in addition the properties of solutions are different in the critical exponent case our purpose is to answer an open problem proposed by bandle et al for the critical exponent case and it together with the one obtained by them shows that the critical exponent case does belong to the non blow up case which is completely different from the case in euclidean space

a comparative study of transformation functions for nonrigid image registration transformation functions play a major role in nonrigid image registration in this paper the characteristics of thin plate spline tps multiquadric mq piecewise linear pl and weighted mean wm transformations are explored and their performances in nonrigid image registration are compared tps and mq are found to be most suitable when the set of control point correspondences is not large fewer than a thousand and variation in spacing between the control points is not large when spacing between the control points varies greatly pl is found to produce a more accurate registration than tps and mq when a very large set of control points is given and the control points contain positional inaccuracies wm is preferred over tps mq and pl because it uses an averaging process that smoothes the noise and does not require the solution of a very large system of equations use of transformation functions in the detection of incorrect correspondences is also discussed

the morse smale property for a semi linear parabolic equation on etudie la dynamique d equations aux derivees partielles paraboliques semi lineaires du type suivant u t u xx f x u 0 0 u 0 t u 1 t 0 t 0 u x 0 x

global nonexistence for the cauchy problem of some nonlinear reaction diffusion systems we first consider the parabolic equationut 2um a x uq f t x u p w t x t 0 x rn where 2 is the 2 fractional power of the laplacian which for 0 2 stands for impurities and f t x and w t x are given nonnegative functions and find its critical exponent then we consider the criticality for five systems of strongly coupled parabolic equations two of them with nonlinear convective terms our results answer positively some open problems raised recently by bandle deng levine and zhang

on the critical fujita exponents for solutions of quasilinear parabolic inequalities abstract this work is devoted to the study of critical blow up phenomena for wide classes of quasilinear parabolic equations and inequalities the model example for this treatment is well known and comes from the theory of turbulent diffusion u t div x u m 1 u x 2 u m 1 u x u q 1 u m 1 1 we obtain the existence of critical blow up exponents for nonnegative weak solutions of inequalities of the type that belong only locally to the corresponding sobolev spaces in the half space r 1 r n n 1 we impose no conditions on the behavior of solutions on the hyperplane t 0 so that the results obtained in the paper are of liouville type the approach developed herein is directly applicable to the study of analogous problems for systems of quasilinear elliptic and parabolic equations and inequalities and its elliptic analogue has recently been developed by the authors

blow up for quasilinear heat equations with critical fujita s exponents we consider the cauchy problem for the quasilinear heat equationwhere 0 is a fixed constant with the critical exponent in the source term c 1 2 n it is well known that if 1 c then any non negative weak solution u x t 0 blows up in a finite time for the semilinear heat equation he with 0 the above result was proved by h fujita 4 in the present paper we prove that u 0 blows up in the critical case 1 2 n with 0 a similar result is valid for the equation with gradient dependent diffusivitywith 0 and the critical exponent 1 2 n

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

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

necessary and sufficient conditions for complete blow up and extinction for one dimensional quasilinear heat equations we characterize the occurrence of complete or incomplete blow up and extinction for a general quasilinear heat equation of the form he text u t phi u xx pm f u text in r times 0 t in terms of the constitutive functions and f we assume that u 0 for u 0 and that f u 0 for the positive sign before f u in he with f u superlinear as u blow up occurs in finite time supxu x t as t t t i e after the singularity occurs if such continuation exists we say that the blow up extinction is incomplete otherwise it is called complete our characterization is based on the qualitative behaviour of the family of travelling wave solutions and a proper use of the intersection comparison argument the analysis applies to other nonlinear models like the equations with gradient dependent diffusivity

the critical fujita number for a semilinear heat equation in exterior domains with homogeneous neumann boundary values let d be a domain in r n with bounded complement and let n 2 for the initial boundary value problem we prove that there are no non trivial global non negative solutions if 0 n p 1 2 and there exist both global non trivial and non global solutions if n p 1 2

self similar subsolutions and blowup for nonlinear parabolic equations abstract for a wide class of nonlinear parabolic equations of the formut u f u u we prove the nonexistence of global solutions for large initial data we also estimate the maximal existence time to do so we use a method of comparison with suitable blowing up self similar subsolutions as a consequence we improve several known results onut u up on generalized burgers equations and on other semilinear equations this method can also apply to degenerate equations of porous medium type and provides a unified treatment for a large class of problems both semilinear and quasilinear

on the blow up of solutions of a convective reaction diffusion equation we study the blow up of positive solutions of the cauchy problem for the semilinear parabolic equation where u is a scalar function of the spatial variable x n and time t 0 a v a 0 1 p and 1 q we show that a if p 1 and 1 q p there always exist solutions which blow up in finite time b if 1 q p min 1 2 n 1 2 q n 1 or if q 1 and 1 p l 2 n then all positive solutions blow up in finite time c if q 1 and p min 1 2 n 1 2 q n 1 then global solutions exist d if q 1 and p 1 2 n then global solutions exist

a nonlinear diffusion system coupled via nonlinear boundary flux abstract in this paper we deal with the global existence and nonexistence of solutions to a nonlinear diffusion system coupled via nonlinear boundary flux by constructing various kinds of sub and super solutions and using the basic properties of m matrix we give the necessary and sufficient conditions for global existence of nonnegative solutions the critical curve of fujita type is conjectured with the aid of some new results which extend the recent results of wang et al nonlinear anal 71 2009 2134 2140 and li et al j math anal appl 340 2008 876 883 to more general equations

blow up solutions of cubic differential systems abstract we investigate the existence problem for blow up solutions of cubic differential systems we find sets of initial values of the blow up solutions we also discuss a method of finding upper estimates for the blow up time of these solutions our approach can be applied to systems of partial differential equations we apply this approach to the cauchy dirichlet problem for systems of semilinear heat equations with cubic nonlinearities

blow up behaviors for semilinear parabolic systems coupled in equations and boundary conditions abstract this paper concerns with blow up behaviors for semilinear parabolic systems coupled in equations and boundary conditions in half space we establish the rate estimates for blow up solutions and prove that the blow up set is r n under proper conditions on initial data furthermore for n 1 more complete conclusions about such two topics are given

piecewise cubic mapping functions for image registration in a recent paper 1 a registration technique was proposed that registered two images by triangulating the images and mapping corresponding triangular regions in the images using a linear function this paper extends the previous technique to include piecewise nonlinear functions as mapping functions a nonlinear mapping function in addition to providing continuous mapping provides smooth transition from one local function to another the obtained mapping function which is a piecewise combination of local mapping functions is therefore continuous and smooth all over a technique based on the clough tocher subtriangulation 2 is described which determines piecewise cubic mapping functions for image registration

an adaptive method for image registration abstract the paper deals with the registration of images with non linear local geometric distortions it describes a new approach to the determination of a mapping function from given coordinates of control points the processed image is recursively divided into subregions of various size and shape according to the distortion character each subregion is then transformed by a simple local transformation the described method enables the registration with optional accuracy a practical use of this method is presented and a comparison of its accuracy and computing complexity with previously published methods is given

critical exponents for a fast diffusive polytropic filtration equation with nonlinear boundary flux abstract in this paper we deal with a fast diffusive polytropic filtration equation u t x u m x p 2 u m x 1 p 1 1 m in r 0 subject to a nonlinear boundary flux u m x p 2 u m x 0 t u q 0 t t 0 we first get the behavior of the solution at infinity and establish the critical global existence exponent and critical fujita exponent for the fast diffusive polytropic filtration equation furthermore give the blow up set and upper bound of the blow up rate for the nonglobal solutions

blow up analysis in quasilinear reaction diffusion problems with weighted nonlocal source abstract in this paper we consider the blow up of solutions to a class of quasilinear reaction diffusion problems g u t u 2 u a x f u in 0 t u u 0 on 0 t u x 0 u 0 x in where is a bounded convex domain in r n n 2 weighted nonlocal source satisfies a x f u x t a 1 a 2 u x t p u x t l d x m and a 1 a 2 p l and m are positive constants by utilizing a differential inequality technique and maximum principles we establish conditions to guarantee that the solution remains global or blows up in a finite time moreover an upper and a lower bound for blow up time are derived furthermore two examples are given to illustrate the applications of obtained results

convergence asymptotic periodicity and finite point blow up in one dimensional semilinear heat equations abstract we consider the initial value problem for the semilinear heat equation u t u xx f u t 0 x l t 0 under the dirichlet the neumann or the periodic boundary conditions we show that each solution whether it exists globally for t 0 or blows up in a finite time possesses an asymptotic profile in a certain sense and tends to this profile as time increases in the special case where f u t t f u t for some t 0 among other things the above statement is interpreted as saying that any bounded global solution converges as t to a time t periodic solution having some specific spatial structure in the case where the solution blows up in a finite time say at t t 0 assuming simply that f is a smooth function satisfying some growth conditions and that the initial data is a nonconstant bounded function we prove that the blow up set is a finite set and that lim t t 0 u x t x exists with being a smooth function having at most finitely many singular points

critical exponents for nonlinear diffusion equations with nonlinear boundary sources abstract this paper is concerned with the large time behavior of solutions to two types of nonlinear diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball we are interested in the critical global exponent q 0 and the critical fujita exponent q c for the problems considered and show that q 0 q c for the multi dimensional porous medium equation and non newtonian filtration equation with nonlinear boundary sources this is quite different from the known results that q 0 q c for the one dimensional case

free vibration analysis of rotating beams by a variable order finite element method the free vibration of rotating beams is analyzed by means of a finite element method of variable order this method entails displacement functions that are a complete power series of a variable number of terms the terms are arranged so that the generalized coordinates are composed of displacements and slopes at the element extremities and additionally displacements at certain points within the element the displacement is assumed to be analytic within an element and thus can be approximated to any degree of accuracy desired by a complete power series numerical results are presented for uniform beams with zero and nonzero hub radii tapered beams and a nonuniform beam with discontinuities since the present method reduces to a conventional beam finite element method for a cubic displacement function the results are compared and found to be superior to the conventional results in terms of accuracy for a given number of degrees of freedom indeed essentially exact eigenvalues and eigenvectors are obtained with this technique which is far more rapidly convergent than other approaches in the literature

on the critical exponent for reaction diffusion equations in this paper we study the initial boundary value problem for u t u h t u p with homogeneous dirichlet boundary conditions where h t t q for large t let s sup s positive solutions w of u t u such that mathop lim sup limits t to infty t s parallel w cdot t parallel infty infty then for p 1 q 1 s we show if p p there are global positive solutions that decay to zero uniformly for t if 1 p p then all nontrivial solutions blow up in finite time we determine p for some conical domains in r 2 and r 3 a similar result is derived for a bounded domain if h t e t for large t

boundedness and blow up for a semilinear reaction diffusion system abstract we consider the semilinear parabolic system s u t u p t u q where x rnn 1 t 0 and p q are positive real numbers at t 0 nonnegative continuous and bounded initial values u0 v0 x are prescribed the corresponding cauchy problem then has a nonnegative classical and bounded solution u t x v t x in some strip st 0 t r n 0 t sup t 0 u v remain bounded in s t we show in this paper that if 0 t so that solutions can be continued for all positive times when pq 1 and 1 pq 1 n 2 with max p q one has t for every nontrivial solution u v t is then called the blow up time of the solution under consideration finally if 1 pq 1 n 2 both situations coexist since some nontrivial solutions remain bounded in any strip s while others exhibit finite blow up times

critical blowup for systems of semilinear wave equations in low space dimensions abstract we consider the cauchy problem for systems of semilinear wave equations in two and three space dimensions with small initial data del santo et al geometric optics and related topics f colombini and n lerner eds progress in nonlinear differential equations and their applications vol 32 pp 117 140 birkhauser boston 1997 have studied the existence and nonexistence of global classical solutions of the cauchy problem except for the critical case in this paper we study the critical case and we show the nonexistence of global classical solutions and also give the upper bounds of the life span

blowup in diffusion equations a survey this paper deals with quasilinear reaction diffusion equations for which a solution local in time exists if the solution ceases to exist for some finite time we say that it blows up in contrast to linear equations blowup can occur even if the data are smooth and well defined for all times depending on the equation either the solution or some of its derivatives become singular we shall concentrate on those cases where the solution becomes unbounded in finite time this can occur in quasilinear equations if the heat source is strong enough there exist many theoretical studies on the question on the occurrence of blowup in this paper we shall recount some of the most interesting criteria and most important methods for analyzing blowup the asymptotic behavior of solutions near their singularities is only completely understood in the special case where the source is a power a better knowledge would be useful also for their numerical treatment thus not surprisingly the numerical analysis of this type of problems is still at a rather early stage the goal of this paper is to collect some of the known results and algorithms and to direct the attention to some open problems

a set of one to one two dimensional biquadratic transformations abstract it is proved that a simple constraint on the parameters of the biquadratic form will produce a set of geometrical transformations that are one to one over a rectangular region of the plane the transformations are treated as interpolations from discrete mappings specified at a finite set of points within the region the constraint which is less stringent than a previously proposed constraint of the same form is shown to be minimal because of their polynomial form these transformations are continuous smooth and computationally simple comparisons with transformations of other forms are made and applications are discussed

bilinear formulation applied to the response and stability of helicopter rotor blade a time finite element method based on hamilton s law of varying action is applied to the analysis of helicopter blade dynamics the bilinear formulation of hamilton s law of varying action is used to discretize the temporal dependence of the equations of motion variable order shape and test functions based on legendre polynomials are used two approaches for the numerical implementation of the bilinear formulation are used one approach obtains the response of a general dynamic system using marching in time the other approach is based on the assumption that the solution is identical at the beginning and end of one period therefore this approach is suitable for periodic systems the bilinear formulation in imposed periodicity mode is used to compute the response of a rigid blade with flap and lag degrees of freedom in forward flight the bilinear formulation in marching mode is applied to find the floquet transition matrix necessary to test the stability of blade motion

on critical exponents for a semilinear parabolic system coupled in an equation and a boundary condition abstract in this paper we consider the system arraycolsep0 14em begin array rcl hskip2em rcl hskip2em c u t delta u v p v whereas if max n 2 there exist both global and nonglobal nonnegative solutions

image interpolation using enhanced multiresolution critical point filters there are increasing demands for image interpolation in various fields such as virtual reality computer animation and video transmission the critical point filters cpf we have proposed previously enable completely automatic matching of two images in our previous method however it has taken a long time to compute the optimal parameter values by iterative searches this paper proposes an improved algorithm called the enhanced critical point filters ecpf where the parameters are stably computed using together the inverse mapping from the destination to the source it takes only a second to match images whose size is 64 64 the algorithm is also improved in its precision by directly handling color images while the previous algorithm has taken only the intensity value into account we apply ecpf to keyframe interpolation of video sequences we also apply ecpf to interpolating two different views of an object to generate any intermediate views in this case there are many constraints that can be used to determine the mapping between the images we propose a method to use such constraints to improve the accuracy of the mappings as the results image based pseudo 3d models are easily created from a set of views without any special devices

the critical curve for a non newtonian polytropic filtration system coupled via nonlinear boundary flux this paper deals with the critical curve of the non newtonian polytropic filtration equation coupled via nonlinear boundary flux the critical global existence curve is obtained by constructing various self similar supersolutions and subsolutions furthermore we get some new results on the critical fujita curve

critical curves of the non newtonian polytropic filtration equations coupled with nonlinear boundary conditions abstract in this paper we consider the existence and non existence of global solutions of the non newtonian polytropic filtration equations with nonlinear boundary conditions we first obtain the critical global existence curve by constructing various self similar supersolutions and subsolutions and then the critical fujita curve is conjectured with the aid of some new results

global existence for nonlinear diffusion equations solutions of nonlinear possibly degenerate reaction diffusion models are known to exist for all time if the asymptotic growth of the reaction term is not greater than that of the diffusion term via concavity methods it is also known that negating such a condition results in solutions which blow up in finite time on the other hand two recent studies regarding the case of linear diffusion have reported on the ability for convective terms in a model to create global existence of solutions where no such result is true in their absence in this paper we develop a theory of global existence for a general class of reaction diffusion convection models which only requires a similar balance of diffusion and reaction our result extends previous work to models including convection but it does not reveal the exact role of convection in yielding global solutions further analysis of a slightly simplified model establishes the global existence of all solutions if the reaction term grows asymptotically at a rate less than that of either diffusion or convection

spline based image registration the problem of image registration subsumes a number of problems and techniques in multiframe image analysis including the computation of optic flow general pixel based motion stereo correspondence structure from motion and feature tracking we present a new registration algorithm based on spline representations of the displacement field which can be specialized to solve all of the above mentioned problems in particular we show how to compute local flow global parametric flow rigid flow resulting from camera egomotion and multiframe versions of the above problems using a spline based description of the flow removes the need for overlapping correlation windows and produces an explicit measure of the correlation between adjacent flow estimates we demonstrate our algorithm on multiframe image registration and the recovery of 3d projective scene geometry we also provide results on a number of standard motion sequences

a new critical phenomenon for semilinear parabolic problems abstract we study the cauchy problem of the inhomogeneous semilinear parabolic equations u up ut w 0 onmn 0 with initial valueu0 0 wheremnis a riemannian manifold with possibly nonnegative ricci curvature there is an exponentp which is critical in the following sense when 1 p the problem has a global positive solution for somew w x 0 and someu0 0