quenching of solutions of parabolic equations with nonlinear boundary conditions in several dimensions on considere le probleme suivant a n dimensions u t au t 0 x u x t 0 t 0 x u x t u x t t 0 x u x 0 0 x ou est un domaine de r n n 2 a est un operateur elliptique lineaire independant du temps est une derivee oblique sur et 1 0 est continument differentiable et croissante et 1

mixed boundary value problems for elliptic and parabolic differential equations of second order on considere les problemes aux valeurs limites mixtes suivants lu f 1 dans mu f 2 sur u f 3 sur avec l operateur elliptique et pu f 1 dans 0 t mu f 2 sur 0 t u f 3 sur 0 t 0 pour des operateurs p paraboliques pour des operateurs obliques generaux m et pour des domaines ou et se rencontrent a des angles arbitraires on montre l existence de solutions classiques quand les angles sont non nuls et f 3 est continue de holder

on a class of higher order methods for simultaneous rootfinding of generalized polynomials using the argument principle higher order methods for simultaneous computation of all zeros of generalized polynomials like algebraic trigonometric and exponential polynomials or exponential sums are derived the methods can also be derived following the continuation principle from 3 thereby the unified approach of 7 is enlarged to arbitrary ordern the local convergence as well as a priori and a posteriori error estimates for these methods are treated on a general level numerical examples are included

le probleme de lehmer en dimension superieure we study a higher dimensional lehmer problem or alternatively the lehmer problem for a power of the multiplicative group more precisely if 1 n are multiplicatively independent algebraic numbers we provide a lower bound for the product of the heights of the i s in terms of the degree d of the number field generated by the i s this enables us to study the successive minima for the height function in a given number field our bound is a generalisation of an earlier result of dobrowolski and is best possible up to a power of log d this in particular shows that the lehmer problem is true for number fields having a small galois group

intersection de sous groupes et de sous varietes i we study the intersection of a subvariety x of an abelian variety a over open image in new window with the union of all the algebraic subgroups of a of given dimension d our main result states that if we remove a suitable exceptional subset from x and if d is small enough then the intersection enjoys a northcott like property the points of bounded height on it form a finite set the condition on d involves only the dimension of x and the structure of a up to isogenies we show how it can be weakened if we assume certain conjectures in the direction of an abelian version of lehmer s problem the theorem is especially meaningful when x is a curve since it is then possible to bound the height and hence to prove finiteness of the set under consideration this generalises the result of e viada on powers of elliptic curves and is analogous to work of e bombieri d masser and u zannier on tori whose general strategy we follow

the transonic shock in a nozzle 2 d and 3 d complete euler systems abstract in this paper we study a transonic shock problem for the euler flows through a class of 2 d or 3 d nozzles the nozzle is assumed to be symmetric in the diverging or converging part if the supersonic incoming flow is symmetric near the divergent or convergent part of the nozzle then as indicated in section 147 of r courant k o friedrichs supersonic flow and shock waves interscience publ new york 1948 there exist two constant pressures p 1 and p 2 with p 1 p 2 such that for given constant exit pressure p e p 1 p 2 a symmetric transonic shock exists uniquely in the nozzle and the position and the strength of the shock are completely determined by p e moreover it is shown in this paper that such a transonic shock solution is unique under the restriction that the shock goes through the fixed point at the wall in the multidimensional setting furthermore we establish the global existence stability and the long time asymptotic behavior of an unsteady symmetric transonic shock under the exit pressure p e when the initial unsteady shock lies in the symmetric diverging part of the 2 d or 3 d nozzle on the other hand it is shown that an unsteady symmetric transonic shock is structurally unstable in a global in time sense if it lies in the symmetric converging part of the nozzle

intersecting subvarieties of abelian varieties with algebraic subgroups of complementary dimension in fact both authors stated stronger conjectures zilber conjectured a finiteness statement for subvarieties that are contained in an improper intersection of x with an algebraic subgroup of s pink was motivated by a more general conjecture in the context of mixed shimura varieties he also showed that conjecture 1 implies the celebrated mordell lang conjecture an important precursor was set in 1999 by bombieri masser and zannier 3 who proved the following result for an algebraic curve c embedded in the algebraic torus gm not contained in the translate of a proper algebraic subgroup and defined over q an algebraic closure of q the set of algebraic points of c which are contained in the union of all algebraic subgroups of codimension at least 1 has bounded absolute weil height they then used their result to show that there are only finitely many points on c contained in the union of all algebraic subgroups of codimension at least 2

a note on simultaneous rootfinding for algebraic exponential and trigonometric polynomials abstract a common derivation and convergence analysis is presented for two methods for the simultaneous computation of all the zeros of an algebraic exponential or trigonometric polynomial the analysis is performed considering a certain class of generalized polynomials which allow a factorization in terms of translations of a function q t such that lagrangian like interpolation is exact the methods were already known for algebraic polynomials q t t but new for exponential q t sinh t 2 and trigonometric polynomials q t sin t 2 using the properties q 0 0 q 0 0 and q 0 0 we prove the local convergence of the methods presented in this note the algorithms only require the evaluation of the generalized polynomial at certain points but no derivatives or coefficients numerical examples are included

second order elliptic equations with mixed boundary conditions we consider the mixed boundary value problem au f in b0u g0 in b1u g1in where is a bounded open subset of rn whose boundary is divided into disjoint open subsets and by an n 2 dimensional manifold in we assume a is a properly elliptic second order partial differential operator on and bj for j 0 1 is a normal jth order boundary operator satisfying the complementing condition with respect to a on the coefficients of the operators and and are all assumed arbitrarily smooth as announced in bull amer math soc 83 1977 391 393 we obtain necessary and sufficient conditions in terms of the coefficients of the operators for the mixed boundary value problem to be well posed in sobolev spaces in fact we construct an open subset t of the reals such that if ds u hs au 0 then for s 12 mod 1 b0 b1 ds hs 12 hs 32 is a fredholm operator if and only if s t moreover t xew tx where the sets tx are determined algebraically by the coefficients of the operators at x if n 2 tx is the set of all reals not congruent modulo 1 to some exceptional value if n 3 tx is either an open interval of length 1 or is empty and finally if n 4 tx is an open interval of length 1

on the explicit torsion anomalous conjecture the torsion anomalous conjecture states that an irreducible variety v embedded in a semi abelian variety contains only finitely many maximal v torsion anomalous varieties in this paper we consider an irreducible variety embedded in a produc of elliptic curves our main result provides a totally explicit bound for the n eron tate height of all maximal v torsion anomalous points of relative codimension one in the non cm case and an analogous effective result in the cm case as an application we obtain the finiteness of such points in addition we deduce some new explicit results in the context of the effective mordell lang conjecture in particular we bound the n eron tate height of the rational points of an explicit family of curves of increasing genus

the perron process applied to oblique derivative problems abstract the perron process has been used with great success to prove the solvability of the dirichlet problem for linear elliptic equations by elementary methods a modification of this process is used to give an elementary proof of the solvability of the regular oblique derivative problem for linear elliptic equations

existence and stability of perturbed transonic shocks for compressible steady potential flows abstract we establish an existence theorem for perturbed transonic steady potential flows where the boundary of the subsonic region consists of a transonic shock and thus the governing equation becomes a free boundary problem we establish gradient estimates and use the fixed point theorem of caristi s which does not require a compactness of the map to establish the existence result we provide new techniques to handle the gradients and show that the flow is strictly elliptic inside of the subsonic region

intermediate schauder theory for second order parabolic equations ii existence uniqueness and regularity on etablit et on demontre des theoremes d existence d unicite et de regularite pour des solutions de problemes aux valeurs limites et initiales paraboliques lineaires dans des espaces de holder ponderes

failure of convergence of the newton weierstrass iterative method for simultaneous rootfinding of generalized polynomials abstract many problems in mathematics and other natural sciences and techniques reduce themselves to determining all roots of generalized polynomial equations we consider in this paper the situations in which the critical initial approximations z i 0 i 1 n fail when the iterative methods of newton weierstrass type are applied

overdetermined weierstrass iteration and the nearest consistent system we propose a generalization of the weierstrass iteration for overdetermined systems of equations and we prove that the proposed method is the gauss newton iteration to find the nearest system which has at least k common roots and which is obtained via a perturbation of prescribed structure in the univariate case we show the connection of our method to the optimization problem formulated by karmarkar and lakshman for the nearest gcd in the multivariate case we generalize the expressions of karmarkar and lakshman and give explicitly several iteration functions to compute the optimum the arithmetic complexity of the iterations is detailed

global transonic conic shock wave for the symmetrically perturbed supersonic flow past a cone in this paper we are concerned with the global existence and stability of a steady transonic conic shock wave for the symmetrically perturbed supersonic flow past an infinitely long conic body the flow is assumed to be polytropic isentropic and described by a steady potential equation theoretically as indicated in r courant k o friedrichs supersonic flow and shock waves interscience publishers inc new york 1948 it follows from the rankine hugoniot conditions and the entropy condition that there will appear a weak shock or a strong shock attached at the vertex of the sharp cone in terms of the different pressure states at infinity behind the shock surface which correspond to the supersonic shock and the transonic shock respectively in the references shuxing chen zhouping xin huicheng yin global shock wave for the supersonic flow past a perturbed cone comm math phys 228 2002 47 84 dacheng cui huicheng yin global conic shock wave for the steady supersonic flow past a cone polytropic case preprint 2006 dacheng cui huicheng yin global conic shock wave for the steady supersonic flow past a cone isothermal case pacific j math 233 2 2007 257 289 and zhouping xin huicheng yin global multidimensional shock wave for the steady supersonic flow past a three dimensional curved cone anal appl 4 2 2006 101 132 the authors have established the global existence and stability of a supersonic shock for the perturbed hypersonic incoming flow past a sharp cone when the pressure at infinity is appropriately smaller than that of the incoming flow at present for the supersonic symmetric incoming flow we will study the global transonic shock problem when the pressure at infinity is appropriately large

a unified approach to methods for the simultaneous computation of all zeros of generalized polynomials applying newton s method to a particular system of nonlinear equations we derive methods for the simultaneous computation of all zeros of generalized polynomials these generalized polynomials are from a function space satisfying a condition similar to haar s condition by this approach we bring together recent methods for trigonometric and exponential polynomials and a well known method for ordinary polynomials the quadratic convergence of these methods is an immediate consequence of our approach and needs not to be proved explicitly moreover our approach yields new interesting methods for ordinary trigonometric and exponential polynomials and methods for other functions occuring in approximation theory

dynamical anomalous subvarieties structure and bounded height theorems abstract according to medvedev and scanlon 14 a polynomial f x q x of degree d 2 is called disintegrated if it is not conjugate to x d or to c d x where c d is the chebyshev polynomial of degree d let n n let f 1 f n q x be disintegrated polynomials of degrees at least 2 and let f 1 f n be the corresponding coordinate wise self map of p 1 n let x be an irreducible subvariety of p 1 n of dimension r defined over q we define the anomalous locus of x which is related to the periodic subvarieties of p 1 n we prove that the anomalous locus of x is zariski closed this is a dynamical analogue of a theorem of bombieri masser and zannier 4 we also prove that the points in the intersection of x with the union of all irreducible periodic subvarieties of p 1 n of codimension r have bounded height outside the anomalous locus of x this is a dynamical analogue of habegger s theorem 8 which was previously conjectured in 4 the slightly more general self maps f 1 f n where each f i q x is a disintegrated rational function are also treated at the end of the paper

on grau s method for simultaneous factorization of polynomials this note is concerned with a a grau s method siam j numer anal 8 1971 pp 425 438 for simultaneous factorization of polynomials as a generalisation of the famous durand kerner method grau s method is discussed on a general level such that certain invariance properties are obtained this yields a matrix interpretation that facilitates error estimates by gershgorin s theorem a convergence result is proved that increases the usual quadratic convergence finally a single step version is stated which has r order of convergence greater than 2