buckling of stochastically heterogeneous beams using a functional perturbation method abstract the buckling load and its probabilistic nature average and variance of bernoulli beams with stochastic material bending stiffness properties is derived analytically by a new functional perturbation method fpm a buckling shape function is assumed based on the homogeneous solution and additional terms to account for the morphology effects the buckling load in the transcendental equation is treated as a functional of the bending modulus stiffness or compliance field applying a functional perturbation to the above equation the buckling load is found analytically to any desired degree of accuracy as a function of material morphology the fpm is executed using both stiffness and compliance statistical data the impact of each of the two data sources on the solution accuracy is examined showing that compliance based solutions are accurate for small correlation lengths statically indeterminate problems can be treated with no additional effort an example of a simply supported beam is solved in detail comparison with previous studies where stochastic finite element and monte carlo simulation were used showed the relative accuracy and insight capabilities of the method the clamped free case is also studied to demonstrate that symmetry conditions used for homogeneous beams to find the buckling load on the basis of a simply supported case are not valid for heterogeneous beams

structure arising from induction and jacquet modules of representations of classical p adic groups jacquet modules are very useful in the study of parabolically induced representations of reductive groups over a p adic field f we shall assume char f 2 in this paper it is very hard to describe explicitly the structure of jacquet modules of parabolically induced representations particularly in the most interesting cases there exists a description of factors of certain filtrations on them that description was done by j bernstein and a v zelevinsky in bz2 and by w casselman in c in the case of general linear groups the functor of parabolic induction and the jacquet functor induce a structure of z graded hopf algebra on the sum r of grothendieck groups of categories of smooth representations of gl n f s of finite length n 0 z1 the multiplication m r r r is defined using parabolic induction while the comultiplication m r r r is defined in terms of jacquet modules the most interesting part of the structure is the property that m r r r is a ring homomorphism hopf axiom this enables one to compute composition series of parabolically induced representations in a very simple way it is interesting to note that the existence of this strong structure did not have serious impact on the development of the representation theory of gl n f one of the reasons for that may lay in the fact that for gl n f there existed a very powerful theory of gelfandkazhdan derivatives and the main results of z1 were obtained using them nevertheless a v zelevinsky showed in z2 that some interesting parts of the representation theory of gl n over a finite field can be obtained as a structure theory of such hopf algebra defined in this setting besides that one of the main tools for the study of representation theory of gl n over a central division f algebra in t1 is such hopf algebra structure in this situation are not available gelfand kazhdan derivatives it is natural to ask does some structure of this kind exist for other simple split classical p adic groups since levi factors of classical groups are isomorphic to direct products of general linear groups and smaller groups from the same series one can expect for such structure to have some relation with r if it exists in the third section we define the direct sum of grothendieck groups r s which corresponds either to the series sp n f n 0 or so 2n 1 f n 0 in a similar way as r was defined for general linear groups the action of r on r s is defined using the parabolic induction in this way r s becomes z graded r module we can make r s a z graded comodule over r the comodule structure map r s r r s is again defined using the jacquet modules similarly as in the case of gl n f it is not hard to see that r s is not a hopf module over r see remark 7 3 in this paper we

jacquet modules of strongly positive representations of the metaplectic group strongly positive discrete series represent a particularly important class of irreducible square integrable representations of p adic groups indeed these representations are used as basic building blocks in known constructions of general discrete series in this paper we explicitly describe jacquet modules of strongly positive discrete series the obtained description of jacquet modules which relies on the classification of strongly positive discrete series given in 10 is valid in both classical and metaplectic case we expect that our results besides being interesting by themselves should be relevant to some potential applications in the theory of automorphic forms where both representations of metaplectic groups and structure of jacquet modules play an important part

on the genericity of cuspidal automorphic forms of so2n 1 this is a sequel of our work js06 we extend moeglin s results m97a and m97b from the even orthogonal groups to old orthogonal groups and complete our proof of the cap conjecture for irreducible cuspidal automoprhic representations of so2n 1 a with special bessel models we also give characterization of the vanishing of the central value of the standard l function of so2n 1 a in terms of theta correspondence as result we obtain the weak langlands functorial transfer from so2n 1 a to gl2n a for irreducible cuspidal automoprhic representations of so2n 1 a with special bessel models

natural frequencies and mode shapes of deterministic and stochastic non homogeneous rods and beams abstract natural frequencies and mode shapes of non homogeneous deterministic and stochastic rods and beams are studied the solution is based on the functional perturbation method fpm the frequencies and mode shapes are considered as functionals of the non homogeneous properties the natural frequency and mode shape of the k th order is obtained analytically to any desired degree of accuracy once the functional derivatives with respect to the non uniform property have been found the solution for any morphology is obtained by direct integration without resolving the differential equation several examples with different non homogeneous properties are solved and compared with exact solutions as an accuracy check the fpm accuracy range for the frequency and the mode shape is less than 1 even for high heterogeneities in the stochastic case the accuracy of the natural frequencies depends on the stochastic information used given on the correlation distance roughly the grain size on the function around which the perturbation is executed and on whether we are interested in the properties of or of 2 moreover all frequency modes have the same response to heterogeneity as long as their wave length is of the order of the heterogeneity s characteristic distance in addition the heterogeneity effect on the average natural frequencies is minimal for the fundamental mode and may serve as a design tool

effect of strength modulus correlation on reliability of randomly heterogeneous beams abstract the strength reliability of linearly elastic brittle stochastically heterogeneous beams is studied on the basis of the weakest link approach the analysis is formulated by a functional perturbation method resulting in an analytical solution of the failure probability of the beam heterogeneity material morphology is random and confined to longitudinal direction only under bernoulli assumptions the problem is statically indeterminate and external loads are not random the stress field is random and functionally dependent on morphology in particular local strength is also a function of modulus therefore the strength reliability of the beam is morphology dependent both through static indeterminacy and local strength modulus correlation the above is also coupled with the probabilistic nature of strength associated with surface defects and irregularities the case of single indeterminacy clamped simply supported beam is investigated for simplicity it is shown that the strength of the beam is significantly affected by material morphology and that the effect can be either positive increased strength or negative depending on the strength moduli correlation for example for an effective grain size of l 10 and a compliance statistical variance of 1 12 the morphology effect on the allowable design load was found to be in the order of 10 calculation of size effect corresponding to strength showed a complex non classical grain size dependency

entire solutions of time periodic bistable reaction advection diffusion equations in infinite cylinders this paper is concerned with the existence and some qualitative properties of entire solutions for a reaction advection diffusion equation in infinite cylinders with time periodic bistable nonlinearity here an entire solution means a solution defined in the whole space and for all time t by the comparison principle coupled with the supersolution and subsolution technique it is proved that there exists an entire solution furthermore it is shown that such an entire solution is unique and liapunov stable unlike the reaction diffusion equation without advection the lack of symmetry between increasing and decreasing traveling fronts caused by the advection affects the construction of supersolutions and subsolutions

liouville type results for a nonlocal obstacle problem this paper is concerned with qualitative properties of solutions to nonlocal reaction diffusion equations of the form int mathbb r n setminus k j x y big u y u x big d y f u x 0 quad x in r n setminus k set in a perforated open set mathbb r n setminus k where k subset mathbb r n is a bounded compact obstacle and f is a bistable nonlinearity when k is convex we prove some liouville type results for solutions satisfying some asymptotic limiting conditions at infinity we also establish a robustness result assuming slightly relaxed conditions on k

pulsating type entire solutions of monostable reaction advection diffusion equations in periodic excitable media abstract we establish the existence of pulsating type entire solutions of reaction advection diffusion equations with monostable nonlinearities in a periodic framework here the nonlinearities include the classic kpp case the pulsating type entire solutions are defined in the whole space and for all time t r by studying a pulsating traveling front connecting a constant unstable stationary state to a stable stationary state which is allowed to be a positive function we proved that there exist pulsating type entire solutions behaving as two pulsating traveling fronts coming from both directions and approaching each other the key techniques are to characterize the asymptotic behavior of the solutions as t in terms of appropriate subsolutions and supersolutions

entire solutions to reaction diffusion equations in multiple half lines with a junction abstract there exists a traveling front wave to a bistable reaction diffusion equation in a whole line under a certain condition of reaction term f u we deal with the bistable reaction diffusion equation with the same f u in a domain which is a graph of special type that is a union of half lines starting at a common point so the domain has a unique junction of the half lines the aim of our study is to show the existence of nontrivial entire solutions which are classical solutions defined for all x t r we prove that there are entire solutions which converge to the front waves in some of half lines and converge to zero in the remaining half lines as t we also give a condition under that the entire solutions exhibit the blocking of the front propagation this blocking is caused by the emergence of stationary solutions the stability instability of the stationary solutions are proved

bessel models for gsp 4 methods of theta correspondence are used to analyze local and global bessel models for gsp 4 proving a conjecture of gross and prasad which describes these models in terms of local epsilon factors in the local case and the non vanishing of central critical l value in the global case

generalized transition waves and their properties in this paper we generalize the usual notions of waves fronts and propagation speeds in a very general setting these new notions which cover all usual situations involve uniform limits with respect to the geodesic distance to a family of hypersurfaces that are parametrized by time we prove the existence of new such waves for some time dependent reaction diffusion equations as well as general intrinsic properties some monotonicity properties and some uniqueness results for almost planar fronts the classification results which are obtained under some appropriate assumptions show the robustness of our general definitions 2012 wiley periodicals inc

statistical modeling of heterogeneous micro beams statistical characteristics averages and variances of heterogeneous small size beams micro beams composed of micro elements grains of randomly distributed stiffness isotropic is studied only longitudinal variations are considered element to beam size length ratio is not negligible and the use of an equivalent homogeneous structure with the classical effective material properties is not sufficient using standard statistical tools probability density and correlation functions it is shown that for indeterminate cases even average deflections obtained explicitly are load dependent and are not identical with their corresponding homogeneous case bounds for the statistical dispersion of deflections and reaction forces are found analytically for some cases of weak heterogeneity it is shown that dispersion parameters for indeterminate problems can be obtained by superposition using both averages and dispersion data of corresponding determinate cases leading to reciprocal type relations

twisted endoscopy and reducibility of induced representations for p adic groups 1 introduction this is the first in a series of papers in which we study the reducibility of representations induced from discrete series representations of the levi factors ofmaximal parabolic subgroups of p adic groups on the unitary axis the problem is equivalent to determining certain local langlands l functions which are of arithmetic significance by themselves one of the main aims of this paper is to interpret our results in the direction of the parametrization problem by means of the theory of twisted endoscopy for which our method seems to be very suitable when the representation is supercuspidal we also study the reducibility of the induced representations off the unitary axis let f be a p adic field of characteristic zero fix a positive integer n 1 and let g be either of the groups sp2n s02n or s02n l in all three cases there is a conjugacy class of maximal parabolic subgroups which has gl as its levi factor let p mn be the standard parabolic subgroup ofg in this conjugacy class then m gl let tr be a discrete series representation of m gln f and given s c let i s tr be the representation of g g f induced from tr r idet ls let i tr i 0 tr

the saito kurokawa lifting and functoriality certain nontempered liftings from pgl 2 pgl 2 to pgsp 4 are constructed using the theory of local and global theta lifts the resulting representations on pgsp 4 are the saito kurokawa representations the lifting is shown to be functorial under certain reasonable assumptions on the local langlands correspondence for pgsp 4

strongly positive representations of gspin_ 2n 1 and the jacquet module method we explicitly construct the structure of jacquet modules of parabolically induced representations of gspin 2n 1 over a p adic field f of any characteristic using this construction of the jacquet module we obtain a classification of strongly positive representations of gspin 2n 1 over f and describe the general discrete series representations of gspin 2n 1 over f assuming the half integer conjecture one application of this paper is the proof of the equality of l functions from the langlands shahidi method and artin l functions through the local langlands correspondence kim in langlands shahidi l functions for gspin groups and the generic arthur packet conjecture preprint

front blocking versus propagation in the presence of drift term varying in the direction of propagation abstract in this paper we derive quantitative conditions under which a compactly supported drift term depending on the direction of propagation blocks a traveling wave solution or lets it pass almost unchanged we give explicit conditions on the drift term for blocking as well as almost unchanged propagation in one spatial dimension

bistable transition fronts in rn abstract this paper is chiefly concerned with qualitative properties of some reaction diffusion fronts the recently defined notions of transition fronts generalize the standard notions of traveling fronts in this paper we show the existence and the uniqueness of the global mean speed of bistable transition fronts in r n this speed is proved to be independent of the shape of the level sets of the fronts the planar fronts are also characterized in the more general class of almost planar fronts with any number of transition layers these qualitative properties show the robustness of the notions of transition fronts but we also prove the existence of new types of transition fronts in r n that are not standard traveling fronts thus showing that the notions of transition fronts are broad enough to include other relevant propagating solutions

front blocking in the presence of gradient drift abstract this paper tries to understand how a drift influences the wave propagation of a bistable reaction diffusion equation in straight cylinders in dimension n 3 we derive a quantitative condition under which a compactly supported drift term blocks the propagation of a traveling wave we assume for this that the drift has a potential

optimized functional perturbation method and morphology based effective properties of randomly heterogeneous beams abstract a functional perturbation method fpm has been recently developed for the analysis of stochastically heterogeneous structures for which the heterogeneity scale is not negligible relative to the macro dimensions the fpm is based on considering the target function here the buckling load p as a functional of the stochastic morphology the target function is written as a functional perturbation series near a convenient homogeneous property usually stiffness k or compliance s thus the accuracy depends on the choice of the property around which the perturbation is carried out an optimized fpm ofpm is presented here which concentrates on finding a property k which is a function of k or s such that the target function converges faster this is accomplished by looking for k which minimizes or nulls if possible the second term in the functional perturbation series besides its improved accuracy has also a dual meaning which is related to the notion of effective property however the effectiveness is weak since the property is not purely material but depends on external loading shapes an example of a buckling problem is examined in detail for which is found analytically as a simple power of k which directly depends on morphology comparing the new ofpm with previous fpm and numerical monte carlo finite element results shows the desired improved accuracy the advantages of the ofpm are then shown and discussed

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

a proof of langland s conjecture on plancherel measures complementary series of p adic groups analysis of p adic reductive groups our first result theorem 7 9 proves a conjecture of langlands on normalization of intertwining operators by means of local langlands root numbers and l functions at least when the group is quasi split and the inducing representation is generic assuming two natural conjectures in harmonic analysis of p adic groups we also prove the validity of the conjecture in general theorem 9 5 as our second result we obtain all the complementary series and special representations of quasi split p adic groups coming from rank one parabolic subgroups and generic supercuspidal represen

generalized fronts in reaction diffusion equations with mono stable nonlinearity abstract we consider transition fronts generalized traveling fronts of mono stable reaction diffusion equations with spatially inhomogeneous nonlinearity by constructing a cutoff function and using an approximate method we establish the existence of transition fronts of the equation furthermore we give the uniform non degeneracy estimates of the solutions such as a lower bound on the time derivative on some level sets as well as an upper bound on the spatial derivative

existence and stability traveling wave solutions for a system of social outbursts abstract we study the existence and stability of planar traveling wave solutions to the system of reaction diffusion equations u t 2 u x 2 u 1 u 1 e v 1 u x r n t 0 v t 2 v x 2 v 1 u p 1 x r n t 0 which was introduced in 8 as a model for the spatiotemporal dynamics of rioting activity and social tension the wave like spread of rioting activity observed in the 2005 french riots 12 motivates the study of these type of solutions which were numerically analyzed in 46 of particular interest is the qualitative difference in traveling wave solutions between the p 0 and p 0 case we present results for the existence and stability of these type of solutions for p 0 and provide the asymptotic approach rates of the traveling wave solutions to the steady states as x for the case of p 0 we study the stability of such solutions using evans functions and a combination of analytical and numerical methods to show irrefutable evidence of spectral stability

pattern formation in a flux limited reaction diffusion equation of porous media type a non linear pde featuring flux limitation effects together with those of the porous media equation non linear fokker planck is presented in this paper we analyze the balance of such diverse effects through the study of the existence and qualitative behavior of some admissible patterns namely traveling wave solutions to this singular reaction diffusion equation we show the existence and qualitative behavior of different types of traveling waves classical profiles for wave speeds high enough and discontinuous waves that are reminiscent of hyperbolic shock waves when the wave speed lowers below a certain threshold some of these solutions are of particular relevance as they provide models by which the whole solution and not just the bulk of it as it is the case with classical traveling waves spreads through the medium with finite speed

on an algebraic approach to the zelevinsky classification for classical p adic groups abstract in this paper we classify irreducible admissible representations of p adic classical groups in a purely algebraic way we present a new and simple algorithm for constructing the classifying data which is also useful in other contexts where the computation with jacquet modules or constant terms of eisenstein series appears we construct and study non standard intertwining operators they are defined in a purely algebraic way although their rationality follows from g muic a geometric construction of intertwining operators for reductive p adic groups manuscripta math 125 2008 241 272

correction to poles and residues of standard l functions attached to siegel modular forms correction to my paper on the poles of standard l functions attached to siegel modular forms

generalized traveling waves in disordered media existence uniqueness and stability we prove existence uniqueness and stability of transition fronts generalized traveling waves for reaction diffusion equations in cylindrical domains with general inhomogeneous ignition reactions we also show uniform convergence of solutions with exponentially decaying initial data to time translations of the front in the case of stationary ergodic reactions the fronts are proved to propagate with a deterministic positive speed our results extend to reaction advection diffusion equations with periodic advection and diffusion

theta dichotomy for unitary groups some recent work of gross and prasad 14 suggests that the root numbers attached to certain symplectic representations of the weil deligne group of a local field f control certain branching rules for representations of orthogonal groups over f on a global level this local phenomenon should have implications for the structure of the value at the center of symmetry for certain l functions of arithmetic interest 12 this conjectural picture is based to some extent on the now classic work of tunnell 47 and waldspurger 49 as well as on the case of the triple product l function 13 34 17 in all of these examples the local root number detects the existence of a certain type of invariant linear functional it is possible to set up analogous conjectures for the isometry groups of hermitian or quaternion hermitian forms it turns out that root numbers also play a role in the local and global theta correspondence roughly speaking certain local root numbers should control the occurrence of representations in the local theta correspondence between groups of the same size e g for dual pairs of the form sp n o 2n 1 and u n u n as will be seen the theta correspondence for such pairs is connected with a certain induced representation in s at the point s 0 on the unitary axis by contrast the correspondence for the pairs sp n o 2n and sp n o 2n 2 discussed by prasad 35 is connected to the behavior of a similar induced representation at the points 12 in which case no epsilon factor arises in this paper we consider the local theta correspondence for unitary groups in the non archimedean case let f be a non archimedean local field of characteristic not equal to 2 and let e be a quadratic extension of f for further notation see the notation section at the end of this introduction let v and w be e vector spaces of dimensions m and n equipped respectively with a hermitian form v v e and a skew hermitian form w w e then the isometry groups g v and g w of the spaces v and w form a dual reductive pair in the symplectic group sp w where w v e w viewed as an f vector space of dimension 2mn and equipped with the symplectic form

reduction to real infinitesimal character in affine hecke algebras the main result of this paper is to show that the problem of the determination of the unramified unitary dual of a split p adic group is equivalent to the problem of determining the unitary dual of the corresponding graded hecke algebra in bm the authors established this equivalence in the case of iwahori spherical representations under a certain restriction namely it was essential for the infinitesimal character to be real in the terminology of bmj in terms of the langlands deligne lusztig parameters s u p kul the restriction is that s e lg be a purely hyperbolic element the technique used in bm was to combine the notion of the signature of a k character in v with some facts which follow from kl namely that the 2w characters of tempered representations are linearly independent this is essentially true precisely when the infinitesimal character is real for if not s has an elliptic part se such that

the zelevinsky classification of unramified representations of the metaplectic group abstract in this paper a zelevinsky type classification of genuine unramified irreducible representations of the metaplectic group over a p adic field with p 2 is obtained the classification consists of three steps firstly it is proved that every genuine irreducible unramified representation is a fully parabolically induced representation from unramified characters of general linear groups and a genuine irreducible negative unramified representation of a smaller metaplectic group genuine irreducible negative unramified representations are described in terms of parabolic induction from unramified characters of general linear groups and a genuine irreducible strongly negative unramified representation of a smaller metaplectic group finally genuine irreducible strongly negative unramified representations are classified in terms of jordan blocks the main technical tool is the theory of jacquet modules

local minimisers and singular perturbations we construct local minimisers to certain variational problems the method is quite general and relies on the theory of convergence the approach is demonstrated through the model problem it is shown that in certain nonconvex domains n and for e small there exist nonconstant local minimisers u e satisfying u e 1 except in a thin transition layer the location of the layer is determined through the requirement that in the limit u e u 0 the hypersurface separating the states u 0 1 and u 0 1 locally minimises surface area generalisations are discussed with for example vector valued u and anisotropic perturbations replacing u 2

on the non unitary unramified dual for classical p adic groups in this paper we give a zelevinsky type classification of unramified irreducible representations of split classical groups

construction of discrete series for classical p adic groups in this paper the authors complete the classification of irreducible square integrable representations of classical p adic groups assuming a natural assumption which is expected to hold in general this classification implies a parameterization of irreducible tempered representations of these groups and it implies a classification of the non unitary duals of these groups modulo cuspidal data

traveling waves with multiple and nonconvex fronts for a bistable semilinear parabolic equation we construct new examples of traveling wave solutions to the bistable and balanced semilinear parabolic equation in input amssym bbb r n 1 our first example is that of a traveling wave solution with two non planar fronts that move with the same speed our second example is a traveling wave solution with a nonconvex moving front to our knowledge no existence results of traveling fronts with these type of geometric characteristics have been previously known our approach explores a connection between solutions of the semilinear parabolic pde and eternal solutions to the mean curvature flow in input amssym bbb r n 1

a regularized siegel weil formula for unitary groups for the quasi split unitary group u n n we prove a refined analogue of the result of s s kudla and s rallis on an identity a regularized siegel weil formula between a residue of an eisenstein series and the integral of a certain theta function

transition fronts of time periodic bistable reaction diffusion equations in rn abstract this paper is concerned with the existence and qualitative properties of transition fronts for time periodic bistable reaction diffusion equations in r n we first show that any almost planar transition front is actually planar regardless of the number of transition layers then we prove that all transition fronts admit a global mean speed and it holds c where c is the speed of the planar traveling front finally we establish the existence of a transition front in r n that is not a standard traveling front such a front behaves like three moving time periodic planar fronts as time goes to and like a time periodic v shaped traveling front as time goes to

a new functional perturbation method for linear non homogeneous materials abstract a functional perturbation method fpm for solving boundary value problems of linear materials with non homogeneous properties is introduced the fpm is based on considering the unknown field such as displacements or temperatures as a functional of the non uniform property i e elastic modulus or thermal conductivity the governing differential equations are expanded functionally by frechet series leading to a set of differential equations with constant coefficients from which the unknown field is found successively to any desirable degree of accuracy a unique property of the fpm is that once the frechet functions are found the solution for any morphology is obtained by direct integration without re solving the differential equation for each case the fpm procedure is outlined first for general linear differential equations with non uniform coefficients then four examples are solved and discussed a 1d tensile loading of a rod with continuously varying and discontinuous moduli beam bending beam deflection on non uniform elastic foundation and a unidirectional heat conduction problem fpm results are compared with the exact if exists or numerical solution the fpm accuracy for the bending problem is also compared to the common rayleigh ritz and galerkin methods it is shown that the fpm is inherently more accurate since the convergence rate of the other methods depends on the arbitrarily chosen shape functions while in the fpm these functions are obtained as generic results of each order of the solution the fpm solution is analytical and is shown to be suitable for large variations in material properties thus a direct insight of each functional perturbation order is possible advantages and limitations of the fpm as compared to other existing methods are discussed in detail

bistable traveling waves around an obstacle we consider traveling waves for a nonlinear diffusion equation with a bistable or multistable nonlinearity the goal is to study how a planar traveling front interacts with a compact obstacle that is placed in the middle of the space n as a first step we prove the existence and uniqueness of an entire solution that behaves like a planar wave front approaching from infinity and eventually reaching the obstacle this causes disturbance on the shape of the front but we show that the solution will gradually recover its planar wave profile and continue to propagate in the same direction leaving the obstacle behind whether the recovery is uniform in space is shown to depend on the shape of the obstacle 2008 wiley periodicals inc

random field models of heterogeneous materials abstract one of the main challenges in solid mechanics lies in the passage from a heterogeneous microstructure to an approximating continuum model in many cases e g stochastic finite elements statistical fracture mechanics the interest lies in resolution of stress and other dependent fields over scales not infinitely larger than the typical microscale this may be accomplished with the help of a meso scale window which becomes the classical representative volume element rve in the infinite limit it turns out that the material properties at such a mesoscale cannot be uniquely approximated by a random field of stiffness compliance with locally isotropic realizations but rather two random continuum fields with locally anisotropic realizations corresponding respectively to essential and natural boundary conditions on the meso scale need to be introduced to bound the material response from above and from below we study the first and second order characteristics of these two meso scale random fields for anti plane elastic response of random matrix inclusion composites over a wide range of contrasts and aspect ratios special attention is given to the convergence of effective responses obtained from the essential and natural boundary conditions which sheds light on the minimum size of an rve additionally the spatial correlation structure of the crack density tensor with the meso scale moduli is studied

a heteroclinic orbit connecting traveling waves pertaining to different nonlinearities in a channel with decreasing cross section abstract in this paper we consider a semilinear parabolic equation in an infinite cylinder with shrinking cross section the portion where the domain is not a straight half cylinder is assumed to be compact the spatially varying nonlinearity is such that it connects two spatially independent bistable nonlinearities in a compact set in space we prove that given such a setting a traveling wave obeying the equation with the one bistable nonlinearity and starting at the respective side of the decreasing cylinder will converge to a traveling wave solution prescribed by the nonlinearity on the other side

asymptotic behavior of solutions of semilinear elliptic equations in unbounded domains two approaches abstract in this paper we study the asymptotic behavior as x 1 of solutions of semilinear elliptic equations in quarter or half spaces for which the value at x 1 0 is given we prove the uniqueness and characterize the one dimensional or constant profile of the solutions at infinity to do so we use two different approaches the first one is a pure pde approach and it is based on the maximum principle the sliding method and some new liouville type results for elliptic equations in the half space or in the whole space r n the second one is based on the theory of dynamical systems

entire solutions in monostable reaction advection diffusion equations in infinite cylinders abstract this paper is concerned with entire solutions of a monostable reaction advection diffusion equation in infinite cylinders without the condition f u f 0 by constructing a quasi invariant manifold we prove that there exist two classes of entire solutions furthermore we show that one class of such entire solutions is unique up to space and time translation

entire solutions of the kpp equation this paper deals with the solutions defined for all time of the kpp equation ut uxx f u 0 0 f 0 1 0i n 0 1 and f 0 s f 0 0 in 0 1 this equation admits infinitely many traveling wave type solutions increasing or decreasing in x i t also admits solutions that depend only on t in this paper we build four other manifolds of solutions one is 5 dimensional one is 4 dimensional and two are 3 dimensional some of these new solutions are obtained by considering two traveling waves that come from both sides of the real axis and mix furthermore the traveling wave solutions are on the boundary of these four manifolds c 1999 john wiley sons inc

a heteroclinic orbit connecting traveling waves pertaining to different nonlinearities abstract in this paper we consider a semilinear parabolic equation in an infinite cylinder the spatially varying nonlinearity is such that it connects two spatially independent bistable nonlinearities in a compact set in space we prove that given such a setting a traveling wave obeying the equation with the one bistable nonlinearity and starting at the respective side of the cylinder will converge to a traveling wave solution prescribed by the nonlinearity on the other side

strongly positive representations of metaplectic groups abstract in this paper we obtain a classification of irreducible strongly positive square integrable genuine representations of metaplectic groups over p adic fields using a purely algebraic approach our results parallel those of m glin and tadic for classical groups but their work relies on certain conjectures on the other hand our results are complete and there are no additional conditions or hypotheses the important point to note here is that our results and techniques can be used in the case of classical p adic groups in a completely analogous manner

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