aw1 p estimate for solutions to mixed boundary value problems for second order elliptic differential equations on demontre que sous des hypotheses plutot faibles une solution d un probleme aux valeurs limites mixte pour une equation elliptique d ordre 2 est dans l espace de sobolev w 1 p pour p 2

domain dependence of solutions to compressible navier stokes equations the minimization of the drag functional for the stationary isentropic compressible navier stokes equations nse in three spatial dimensions is considered in order to establish the existence of an optimal shape the general result on compactness of families of generalized solutions to the nse is established within in the framework of the modern theory of nonlinear pdes p l lions mathematical topics in fluid dynamics vol 2 compressible models oxford university press clarendon press new york 1998 e feireisl dynamics of viscous compressible fluids oxford university press oxford uk 2004 the family of generalized solutions to the nse is constructed over a family of admissible domains mathcal u ad any admissible domain omega b setminus s contains an obstacle s e g a wing profile compactness properties of the family of admissible domains in the form of the condition mathcal h omega is imposed roughly speaking the condition mathcal h omega is satisfied provided that for any sequence of admissible domains omega n subset mathcal u ad there is a subsequence convergent both in hausdorff metrics and in the sense of kuratowski and mosco the analysis is performed for the adiabatic constant gamma 1 in the pressure law p rho rho gamma and it is based on the technique used in p i plotnikov and j sokolowski comm math phys 258 2005 pp 567 608 in the case of discretized nse the result is a generalization to the stationary equations with gamma 1 of the results obtained in e feireisl a h novotny and h petzeltova math methods appl sci 25 2002 pp 1045 1073 e feireisl appl math optim 47 2003 pp 59 78 for evolution equations within the range gamma 3 2 for the adiabatic ratio

o n log n procedures for tightening cover inequalities abstract we present two procedures for tightening cover induced inequalities in 0 1 programs by using knapsack constraints plus some other information from the program the tightening is obtained by solving successive knapsack problems with all 0 1 objective function coefficients and using dominance criteria to avoid the explicit solving of some knapsack problems the new constraints are 0 1 equivalent to and lp tighter than the original ones both procedures have o n log n complexity where n is the number of variables with nonzero coefficients in the knapsack constraint however one of them can strongly reduce the computational effort some computational experience is reported

multiplicity results for semilinear elliptic problems at resonance and with jumping nonlinearities abstract in the present paper we develop a method to deal with multiple existence of solutions of nonlinear elliptic problems and give some multiple existence results for elliptic boundary value problems at resonance and problems with jumping nonlinearities

on the dietrich escudero approach for solving the 0 1 knapsack problem with a 0 1 objective function abstract in this brief note we demonstrate that the dietrich escudero procedure for solving the 0 1 knapsack problem with all 0 1 objective function coefficients is precisely an application of the dantzig algorithm for solving the 0 1 lp knapsack problem plus an appropriate rounding of the solution

strong formulations for mixed integer programming a survey we attempt to motivate and survey recent research on the use of strong valid inequalities and reformulation to solve mixed integer programming problems

solving 0 1 integer programming problems arising from large scale planning models we present methods that are useful in solving some large scale hierarchical planning models involving 0 1 variables these 0 1 programming problems initially could not be solved with any standard techniques we employed several approaches to take advantage of the hierarchical structure of variables ordered by importance and other structures present in the models critical but not sufficient for success was a strong linear programming formulation we describe methods for strengthening the linear programs as well as other techniques necessary for a commercial branch and bound code to be successful in solving these problems

on tightening cover induced inequalities abstract here we describe computationally efficient procedures for tightening cover induced inequalities by using 0 1 knapsack constraints and if available cliques whose variables are included in the cover an interesting application is the case where the cover is implied by the knapsack constraint the tightening is achieved by increasing the coefficients of the cover inequality the new constraint is 0 1 equivalent to and lp tighter than the original one the computational complexity of the procedures is o n log n where n is the number of variables in the cover

new approach to the incompressible maxwell boussinesq approximation existence uniqueness and shape sensitivity abstract the boussinesq approximation to the fourier navier stokes f n s flows under the electromagnetic field is considered such a model is the so called maxwell boussinesq approximation we propose a new approach to the problem we prove the existence and uniqueness of weak solutions to the variational formulation of the model some further regularity in w 1 2 0 is obtained for the weak solutions the shape sensitivity analysis by the boundary variations technique is performed for the weak solutions as a result the existence of the strong material derivatives for the weak solutions of the problem is shown the result can be used to establish the shape differentiability for a broad class of shape functionals for the models of fourier navier stokes flows under the electromagnetic field

thermally coupled magnetohydrodynamics flow abstract this paper deals with the questions of existence and uniqueness of solutions to the equations of stationary incompressible magnetohydrodynamics mhd when bouyancy effects due to temperature differences in the flow cannot be neglected to that effect we couple the mhd equations to the heat equation and employ the well known boussinesq approximation we consider the equations posed on a bounded three dimensional domain we point out that these equations model such phenomena as the cooling of nuclear reactors by electrically conducting fluids continuous metal casting crystal growth and semiconductor manufacture

on existence regularity and uniqueness of thermally coupled incompressible flows in a system of three dimensional pipes abstract we study an initial boundary value problem for time dependent flows of heat conducting viscous incompressible fluids in a system of three dimensional pipes on a time interval 0 t we are motivated by the bounded domain approach with do nothing boundary conditions in terms of the velocity pressure and temperature of the fluid such flows are described by a coupled parabolic system with strong nonlinearities and including the natural boundary conditions for the velocity and temperature of the fluid on the part of the boundary where the fluid is supposed to leave the channel the present analysis is devoted to the proof of the existence regularity and uniqueness of the solution for the problem described above

some mathematical questions related to the mhd equations some questions relating to the large time behavior of the solutions of mhd equations for a viscous incompressible resistive fluid are investigated the physical system is briefly described and the functional setting of the equations a flow in a bounded domain or in whole space with a space periodicity property in all directions the main existence and uniqueness results for weak and strong solutions of the mhd equations are recalled regularity properties and bounds on the solutions to the equations which are valid for all time are established and the concept of functional invariant sets is introduced which is contained in the space of smooth functions if the data are sufficiently regular the squeezing property of the trajectories are stated and it is shown that any functional invariant set for the mhd equations and in particular any attractor has a finite haussdorf dimension the flow is found to be totally determined for large dimensions by a finite number of parameters 26 references

a branch and cut algorithm for the resolution of large scale symmetric traveling salesman problems an algorithm is described for solving large scale instances of the symmetric traveling salesman problem stsp to optimality the core of the algorithm is a polyhedral cutting plane procedure that exploits a subset of the system of linear inequalities defining the convex hull of the incidence vectors of the hamiltonian cycles of a complete graph the cuts are generated by several identification procedures that have been described in a companion paper whenever the cutting plane procedure does not terminate with an optimal solution the algorithm uses a tree search strategy that as opposed to branch and bound keeps on producing cuts after branching the algorithm has been implemented in fortran two different linear programming lp packages have been used as the lp solver the implementation of the algorithm and the interface with one of the lp solvers is described in sufficient detail to permit the replication of our experiments computational results are reported with up to 42 stsps with sizes rangin

solving mixed integer programming problems using automatic reformulation in this paper we describe computational experience in solving mixed 0 1 programming problems using strong valid inequalities as cutting planes in particular we report on the solution to optimality of 18 medium to large size problems including production planning problems with setup costs and capacity constraints multilevel distribution planning problems drainage and heating system design problems and electricity generator scheduling problems the solution approach uses the theory of strong valid inequalities that we developed in a series of earlier papers here we report specifically on the implementation of an experimental system mpsarx which consists of the sciconic mathematical programming system and an automatic reformulation executor arx that use this theory and on the results obtained with this system

easily computable facets of the knapsack polytope it is known that facets and valid inequalities for the knapsack polytope p can be obtained by lifting a simple inequality derived from each minimal cover we study the computational complexity of such lifting in particular we show that the task of computing a lifted facet can be accomplished in o ns where s n is the cardinality of the minimal cover also for a lifted inequality with integer coefficients we show that the dual tasks of recognizing whether the inequality is valid for p or is a facet of p can be done within the same time bound

on coupled navier stokes and energy equations in exterior like domains we investigate a class of nonlinear evolution systems modeling time dependent flows of incompressible viscous and heat conducting fluids with temperature dependent transport coefficients in three dimensional exterior like domains we prove a local existence theorem for the fully coupled parabolic system with a source term involving the square of the velocity gradient and a combination of dirichlet and artificial boundary conditions