optimal birth control for an age dependent n dimensional food chain model abstract in this paper we investigate optimal policies for an age dependent n dimensional food chain model which is controlled by fertility by using dubovitskii milyutin s general theory the maximum principles are obtained for problems with free terminal states infinite horizon and target sets respectively

an adaptive multitime multigrid algorithm for time periodic flow simulations the multiscale behaviour and multidisciplinary nature of rotorcraft aerodynamics has delayed the introduction of cfd techniques for rotorcraft aerodynamics the numerical dissipation of standard cfd algorithms may destroy tip vortices before blade vortex interaction takes place more advanced cfd algorithms using high order discretization and or local grid refinement are better suited to tackle the problem these algorithms however generally increase the computational complexity of the simulation and their efficiency should be improved before they can be applied to rotorcraft aerodynamics in this paper a four dimensional solution algorithm will be presented which significantly improves the efficiency by exploiting the periodic nature of rotor flows the efficiency of the algorithm is attained by changing a dynamic problem into a static problem which simplifies the coupling with other models blade dynamics and elastics rotor trim allows local grid refinement in space and time without dynamic load balancing issues and solves a periodic problem by construction a three dimensional multigrid algorithm for dg discretisations on curvilinear structured meshes is extended to four dimensional curvilinear meshes with local grid refinement simulations for an oscillating airfoil in subsonic and transonic conditions confirm the performance of the multigrid algorithm and its insensitiveness to highly irregular grid features the temporal stability restriction of the pseudo time step is removed by treating the diagonal term of the time derivative implicitly

on the controllability of the lotka mckendrick model of population dynamics abstract in this work we consider the problem of exact controllability of the linear lotka mckendrick model of population dynamics we establish an observability inequality and show that any initial condition can be steered into any quasi steady state by a distributed control except for a small interval of ages near zero in contrast with that we observe that the boundary control is more efficient in the sense that it controls the entire population the biological implication of our conclusions is that a closed population is more efficiently controlled through birth control as opposed to migration and eradication in particular this supports the trap alter release method for controlling a population of stray cats as opposed to the trap and kill method

solvability of the divergence equation implies john via poincare inequality abstract let r 2 be a bounded simply connected domain we show that for a fixed every p 1 the divergence equation div v f is solvable in w 0 1 p 2 for every f l 0 p if and only if is a john domain if and only if the weighted poincare inequality u x u q d x c u x q dist x q d x holds for some every q 1 this gives a positive answer to a question raised by russ 2013 in the case of bounded simply connected domains in higher dimensions similar results are proved under some additional assumptions on the domain in question

solutions of the divergence operator on john domains if rn is a bounded domain the existence of solutions u w01 p of divu f for f lp with vanishing mean value and 1 p is a basic result in the analysis of the stokes equations it is known that the result holds when is a lipschitz domain and that it is not valid for domains with external cusps in this paper we prove that the result holds for john domains our proof is constructive the solution u is given by an explicit integral operator acting on f to prove that u w01 p we make use of the calderon zygmund singular integral operator theory and the hardy littlewood maximal function for domains satisfying the separation property introduced in s buckley p koskela sobolev poincare implies john math res lett 2 5 1995 577 593 and 1 p n we also prove a converse result thus characterizing in this case the domains for which a continuous right inverse of the divergence exists in particular our result applies to simply connected planar domains because they satisfy the separation property

optimal birth control of age dependent competitive species abstract this work is concerned with optimal policies for two age structured biological populations in a competing system which is controlled by fertilities the maximum principles for problems with free terminal infinite horizon and target sets are obtained respectively via dubovitskii milyutin s general extremal theory

optimal birth control of population dynamics abstract we study optimal birth control policies for an age structured population of mckendrick type which is a distributed parameter system involving first order partial differential equations with nonlocal bilinear boundary control the functional analytic approach of dubovitskii and milyutin is adopted in the investigation maximum principles for problems with a free end condition a fixed final horizon are developed and the time optimal control problem the problem with target sets and the infinite planning horizon case are investigated

hardy sobolev spaces on strongly lipschitz domains of rn let be a strongly lipschitz domain of rn the hardy spaces hr1 and hz1 have been introduced by miyachi studia math 95 3 1990 205 jonsson et al studia math 80 2 1984 141 and chang et al j funct anal 114 1993 286 we first investigate spaces of functions in l1 whose gradients belong to hr1 or hz1 which we call hardy sobolev spaces following strichartz coll math 60 61 1 1990 129 secondly if l a is a uniformly elliptic second order divergence operator on with measurable complex coefficients subject to the dirichlet or the neumann boundary condition we compare the norms of l1 2f and f in suitable hardy spaces on depending on the boundary condition under the assumption that the heat kernel of l satisfies suitable estimates

uniformly fat sets in this paper we study closed sets e which are locally uniformly fat with respect to a certain nonlinear riesz capacity we show that e is actually locally uniformly fat with respect to a weaker riesz capacity two applications of this result are given the first application is concerned with proving sobolev type inequalities in domains whose complements are uniformly fat the second application is concerned with the fekete points of e introduction let x x x2 x be a point in euclidean n space rn with jxl the norm of x for a 0 let i x ixi a n denote the riesz kernel of order a and put i f x f ix y f n f y dy x e r rn ic u x fr yj c n d u y x e r rn when f is a lebesgue integrable function and u a borel measure on rn here dy denotes lebesgue measure on rn if e c rn 0 1 define the a p outer riesz capacity of e by ra p e inf jfllfp ia f 1 on el where if lip is the lebesgue p norm of f we note that a 1 p 2 is the classical newtonian capacity if ap n we let rc p e inf jfjjf j f 1 on el where jc is the truncated riesz kernel defined by je x ixi a n 100 a n x 100 0 lxl 100 we shall say that a property holds a p quasi everywhere abbreviated a p q e on a set e if it holds on e except perhaps for a set of rop capacity zero next we list some properties of riesz capacities to simplify the writing we state these properties only for 0 u l p l 1 a p q e on e and p 1 a p q e on supp u c e moreover e jjli pi ujj rop e received by the editors march 11 1987 1980 mathematic3 subject cla33ification 1985 revi3ion primary 31c15 31b15 1988 american mathematical society 0002 9947 88 1 00 25 per page

optimal birth control of age dependent competitive species ii free horizon problems we study optimal birth policies for two age dependent populations in a competing system which is controlled by fertilities new results on problems with free final time and integral phase constraints are presented and the approximate controllability of system is discussed

optimal harvesting for a nonlinear age dependent population dynamics here we investigate an optimal harvesting problem for a nonlinear age dependent population dynamics existence and uniqueness of a positive solution for the model are demonstrated the structure of the solution is also investigated we establish the existence of the optimal control and the convergence of a certain fractional step scheme for some approximating problems we obtain the optimal controllers in feedback form via the dynamic programming method

overtaking optimal control problem for an age dependent competition system of n species abstract in this paper the overtaking optimal control problem for an age dependent competition model of n species with unbounded time interval is considered the existence of overtaking optimal policy is proved and a maximum principle is carefully derived under less restrictive conditions weak and strong turnpike properties of optimal trajectories are established

on a population dynamics control problem with age dependence and spatial structure we consider the control problem for a population dynamics model with age dependence spatial structure and a nonlocal birth process arising as a boundary condition we examine the controllability at a given time t and show that approximate controllability holds for every fixed finite time t as a consequence a new uniqueness condition continuation result is proved

overtaking optimal control problem of age dependent populations with infinite horizon abstract the optimal birth control of an age dependent population model with unbounded time interval is considered the minimum principle which must be satisfied by the overtaking optimal control is established large time behaviour and the turnpike property of the overtaking optimal trajectory are studied existence results are also presented

a decomposition technique for integrable functions with applications to the divergence problem abstract let r n be a bounded domain that can be written as t t where t t is a countable collection of domains with certain properties in this work we develop a technique to decompose a function f l 1 with vanishing mean value into the sum of a collection of functions f t f t t subordinated to t t such that supp f t f t t and f t f t 0 as an application we use this decomposition to prove the existence of a solution in weighted sobolev spaces of the divergence problem div u f and the well posedness of the stokes equations on holder domains and some other domains with an external cusp arbitrarily narrow we also consider arbitrary bounded domains the weights used in each case depend on the type of domain

korn inequality on irregular domains abstract in this paper we study the weighted korn inequality on some irregular domains e g s john domains and domains satisfying quasihyperbolic boundary conditions examples regarding sharpness of the korn inequality on these domains are presented moreover we show that korn inequalities imply certain poincare inequality

optimal harvesting for periodic age dependent population dynamics here we investigate the optimal harvesting problem for some periodic age dependent population dynamics namely we consider the linear lotka mckendrick model with periodic vital rates and a periodic forcing term that sustains oscillations existence and uniqueness of a positive periodic solution are demonstrated and the existence and uniqueness of the optimal control are established we also state necessary optimality conditions a numerical algorithm is developed to approximate the optimal control and the optimal harvest some numerical results are presented

optimality conditions for age structured control systems abstract we consider a fairly general model extension of the gurtin maccamy model of population dynamics of an age structured control system with nonlocal dynamics and nonlocal boundary conditions a necessary optimality condition is obtained in the form of pontryagin s maximum principle which is applicable to a number of practically meaningful models where the previously known results fail we discuss such models an epidemic control and a capital accumulation model as illustrations

optimal birth control of population dynamics ii problems with free final time phase constraints and mini max costs abstract we study optimal birth control of population systems of mckendrick type which is a distributed parameter system involving first order partial differential equations with nonlocal bilinear boundary control new results on problems with free final time phase constraints and mini max costs are presented