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

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

maximal generalized solution of eikonal equation abstract we study the dirichlet problem for the eikonal equation 1 2 u x 2 a x 0 in u x x on without continuity assumptions on the map a we find a class of maps a contained in the space l for which the problem admits a maximal generalized solution providing a generalization of the notion of viscosity solution

pushdown machines for the macro tree transducer the macro tree transducer can be considered as a system of recursive function procedures with parameters where the recursion is on a tree e g the syntax tree of a program we investigate characterizations of the class of tree tree to string translations which is induced by macro tree transducers macro tree to string transducers respectively for this purpose we define several pushdown machines of which the control is recursive without parameters or even iterative and which work on a generalized pushdown as storage because of the relevance for semantics of programming languages we stress besides the nondeterministic case the study of machines for the total deterministic macro tree to string transducer which translates every input tree into exactly one output tree string respectively finally we characterize the n fold composition of total deterministic macro tree transducers by recursive pushdown machines with an iterated pushdown as storage which is a pushdown of pushdowns of of pushdowns

general existence theorems for hamilton jacobi equations in the scalar and vectorial cases keywords dirichlet problem hamilton jacobi equation existence of solutions reference caa article 1997 002doi 10 1007 bf02392708view record in web of science record created on 2008 11 25 modified on 2017 05 12

a necessary and sufficient condition for strong convergence in sobolev spaces abstract we present an improved version of a necessary and sufficient condition for strong convergence in the sobolev space w 1 p and provide a nontrivial application to a class of fully nonlinear partial differential equations involving the range of the map w 1 p u u p l 1

a diffusive logistic equation with a free boundary and sign changing coefficient in time periodic environment abstract this paper concerns a diffusive logistic equation with a free boundary and sign changing intrinsic growth rate in heterogeneous time periodic environment in which the variable intrinsic growth rate may be very negative in a suitable large region see conditions h1 h2 4 3 such a model can be used to describe the spreading of a new or invasive species with the free boundary representing the expanding front in the case of higher space dimensions with radial symmetry and when the intrinsic growth rate has a positive lower bound this problem has been studied by du guo peng 11 they established a spreading vanishing dichotomy the sharp criteria for spreading and vanishing and estimate of the asymptotic spreading speed in the present paper we show that the above results are retained for our problem

existence and convergence to a propagating terrace in one dimensional reaction diffusion equations we consider one dimensional reaction diffusion equations for a large class of spatially periodic nonlinearities including multistable ones and study the asymptotic behavior of solutions with heaviside type initial data our analysis reveals some new dynamics where the profile of the propagation is not characterized by a single front but by a layer of several fronts which we call a terrace existence and convergence to such a terrace is proven by using an intersection number argument without much relying on standard linear analysis hence on top of the peculiar phenomenon of propagation that our work highlights several corollaries will follow on the existence and convergence to pulsating traveling fronts even for highly degenerate nonlinearities that have not been treated before

storage to tree transducers with look ahead we generalize engelfriet s decomposition result stating that the class of transformations induced by top down tree transducers with regular look ahead is equal to the composition of the class of top down tree transformations and the class of linear tree homomorphisms replacing the input trees with an arbitrary storage type the top down tree transducers are turned into regular storage to tree transducers we show that the class of transformations induced by regular storage to tree transducers with positive look ahead is equal to the composition of the class of transformations induced by regular storage to tree transducers with the class of linear tree homomorphisms we also show that the classes of transformations induced by both io and oi context free storage to tree transducers are closed under positive look ahead and are closed under composition with linear tree homomorphisms

solutions of vectorial hamilton jacobi equations and minimizers of nonquasiconvex functionals abstract we provide a unified approach to prove existence results for the dirichlet problem for hamilton jacobi equations and for the minimum problem for nonquasiconvex functionals of the calculus of variations with affine boundary data the idea relies on the definition of integro extremal solutions introduced in the study of nonconvex scalar variational problem

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

spreading vanishing dichotomy in a diffusive logistic model with a free boundary ii abstract we study the diffusive logistic equation with a free boundary in higher space dimensions and heterogeneous environment such a model may be used to describe the spreading of a new or invasive species with the free boundary representing the expanding front for simplicity we assume that the environment and the solution are radially symmetric in the special case of one space dimension and homogeneous environment this free boundary problem was investigated in du and lin 2010 10 we prove that the spreading vanishing dichotomy established in du and lin 2010 10 still holds in the more general and ecologically realistic setting considered here moreover when spreading occurs we obtain best possible upper and lower bounds for the spreading speed of the expanding front when the environment is asymptotically homogeneous at infinity these two bounds coincide our results indicate that the asymptotic spreading speed determined by this model does not depend on the spatial dimension

a diffusive logistic model with a free boundary in time periodic environment abstract we study the diffusive logistic equation with a free boundary in time periodic environment such a model may be used to describe the spreading of a new or invasive species with the free boundary representing the expanding front for time independent environment in the cases of one space dimension and higher space dimensions with radial symmetry this free boundary problem has been studied in du and lin 2010 12 du and guo 2011 9 in both cases a spreading vanishing dichotomy was established and when spreading occurs the asymptotic spreading speed was determined in this paper we show that the spreading vanishing dichotomy is retained in time periodic environment and we also determine the spreading speed the former is achieved by further developing the earlier techniques and the latter is proved by introducing new ideas and methods

hamilton jacobi equations with state constraints in the present paper we consider hamilton jacobi equations of the form h x u vu 0 x e q where q is a bounded open subset of rn h is a given continuous real valued function of x s p e q x r x rn and vu is the gradient of the unknown function u we are interested in particular solutions of the above equation which are required to be supersolutions in a suitable weak sense of the same equation up to the boundary of q this requirement plays the role of a boundary condition the main motivation for this kind of solution comes from deterministic optimal control and differential games problems with constraints on the state of the system as well from related questions in constrained geodesics

spreading in space time periodic media governed by a monostable equation with free boundaries part 1 continuous initial functions abstract we aim to classify the long time behavior of the solution to a free boundary problem with monostable reaction term in space time periodic media such a model may be used to describe the spreading of a new or invasive species with the free boundary representing the expanding front in time periodic and space homogeneous environment as well as in space periodic and time autonomous environment such a problem has been studied recently in 11 12 in both cases a spreading vanishing dichotomy has been established and when spreading happens the asymptotic spreading speed is proved to exist by making use of the corresponding semi wave solutions the approaches in 11 12 seem difficult to apply to the current situation where the environment is periodic in both space and time here we take a different approach based on the methods developed by weinberger 31 32 and others 16 22 23 24 26 which yield the existence of the spreading speed without using traveling wave solutions in part 1 of this work we establish the existence and uniqueness of classical solutions for the free boundary problem with continuous initial data extending the existing theory which was established only for c 2 initial data this will enable us to develop weinberger s method in part 2 to determine the spreading speed without knowing a priori the existence of the corresponding semi wave solutions in part 1 here we also establish a spreading vanishing dichotomy

the diffusive logistic model with a free boundary in a heterogeneous time periodic environment abstract this paper is concerned with a diffusive logistic model with advection and a free boundary in a spatially heterogeneous and time periodic environment such a model may be used to describe the spreading of a new or invasive species with the free boundary representing the expanding front under more general assumptions on the initial data and the function standing for the intrinsic growth rate of the species sharp criteria for spreading and vanishing are established and estimates for spreading speed when spreading occurs are also derived the obtained results considerably improve and complement the existing ones especially those of 11 25

viscosity solutions almost everywhere solutions and explicit formulas keywords almost everywhere solutions viscosity solutions of nonlinear first order partial differential equations reference caa article 2004 001doi 10 1090 s0002 9947 04 03506 8view record in web of science record created on 2008 11 25 modified on 2017 05 12

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

existence and uniqueness of the solution of a space time periodic reaction diffusion equation this paper is concerned with the study of the periodic solutions and the entire solutions of the equation 1 tu a t x u q t x u f t x u where the diffusion matrix a the advection term q and the reaction term f are periodic in t and x we prove that the sign of the periodic principal eigenvalue associated with the linearized problem determines the existence and the uniqueness of the periodic solution introducing another eigenvalue we are able to state uniqueness conditions for the entire solution and to derive the asymptotic behavior of the solutions of the associated cauchy problem

refined estimates for the propagation speed of the transition solution to a free boundary problem with a nonlinearity of combustion type abstract we are concerned with the nonlinear problem u t u x x f u where f is of combustion type coupled with the stefan type free boundary h t according to 4 5 for some critical initial data the transition solution u locally uniformly converges to which is the ignition temperature of f and the free boundary satisfies h t c t o 1 t for some positive constant c and all large time t in this paper making use of two different approaches we establish more accurate upper and lower bound estimates on h t for the transition solution which suggest that the nonlinearity f can essentially influence the propagation speed

top down tree transducers with two way tree walking look ahead abstract we consider top down tree transducers with deterministic nondeterministic and universal two way tree walking look ahead and compare the transformational powers of their deterministic and strongly deterministic versions by giving the inclusion diagram of the induced tree transformation classes we also study the closure properties of these transformation classes with respect to composition

deterministic top down tree transducers with iterated look ahead it is known that by iterating the look ahead tree languages for deterministic top down tree automata more and more powerful recognizing devices are obtained let dr0 dr where dr is the class of all tree languages recognizable by deterministic top down tree automata and let for n 1 drn be the class of all tree languages recognizable by deterministic top down tree automata with drn 1 look ahead then dr0 dr1 dr2 slutzki and vagvolgyi 1993 showed that the composition powers of the class of all deterministic top down tree transformations with deterministic top down look ahead dttdr form a proper hierarchy i e dttdr n dttdr n 1 for n 0 along the proof they studied the notion of the deterministic top down tree transducer with drn look ahead dttdrn and showed that dttdr n 1 dttdrn n 0 where dttdrn stands for the class of all tree transformations induced by dttdrn s our aim is to show the reversed inclusion i e dttdrn dttdr n 1 n 0 this implies a precise characterization dttdrn dttdr n 1 n 0 and implies that the classes dttdrn n 0 form a proper hierarchy

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author

the stefan problem for the fisher kpp equation abstract we study the fisher kpp equation with a free boundary governed by a one phase stefan condition such a problem arises in the modeling of the propagation of a new or invasive species with the free boundary representing the propagation front in one space dimension this problem was investigated in du and lin 2010 11 and the radially symmetric case in higher space dimensions was studied in du and guo 2011 10 in both cases a spreading vanishing dichotomy was established namely the species either successfully spreads to all the new environment and stabilizes at a positive equilibrium state or fails to establish and dies out in the long run moreover in the case of spreading the asymptotic spreading speed was determined in this paper we consider the non radially symmetric case in such a situation similar to the classical stefan problem smooth solutions need not exist even if the initial data are smooth we thus introduce and study the weak solution for a class of free boundary problems that include the fisher kpp as a special case we establish the existence and uniqueness of the weak solution and through suitable comparison arguments we extend some of the results obtained earlier in du and lin 2010 11 and du and guo 2011 10 to this general case we also show that the classical aronson weinberger result on the spreading speed obtained through the traveling wave solution approach is a limiting case of our free boundary problem here

diffusive kpp equations with free boundaries in time almost periodic environments ii spreading speeds and semi wave solutions abstract in this series of papers we investigate the spreading and vanishing dynamics of time almost periodic diffusive kpp equations with free boundaries such equations are used to characterize the spreading of a new species in time almost periodic environments with free boundaries representing the spreading fronts in the first part of the series we showed that a spreading vanishing dichotomy occurs for such free boundary problems see 16 in this second part of the series we investigate the spreading speeds of such free boundary problems in the case that the spreading occurs we first prove the existence of a unique time almost periodic semi wave solution associated to such a free boundary problem using the semi wave solution we then prove that the free boundary problem has a unique spreading speed

on viscosity solutions of hamilton jacobi equations we consider the dirichlet problem for hamilton jacobi equations and prove existence uniqueness and continuous dependence on boundary data of lipschitz continuous maximal viscosity solutions