La fonctionnelle J sera convexe si et seulement si sa J 0 est une application monotone de V dans V , c'est--a-dire si : admet une solution unique, pp.5-46 ,
48) est une formulation variationnelle d'un probl eme elliptique semi-lin eaire, et puisque n e ue et p e ue sont dans W 1;1 (() alors (5.48) admet une solution unique not ee, pp.3-5 ,
qui appara^ t dans la premi ere equation de (5.47), est minor ee par une constante strictement positive, nous en d eduisons que le probl eme (5.47) poss ede une unique solution (' 1, 3 ) 2 (H 2 DN (()) 3 qui d epend contin^ ument de ,
Quasi???variational inequality and shape optimization for solution of a free boundary problem, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.18, issue.2, pp.143-164, 1999. ,
DOI : 10.1108/03321649910264154
Etude d'un probl eme d'optimisation de forme, pp.25-28, 2000. ,
Sobolev spaces, Academic press, 1975. ,
Connection between nite volume and mixed nite element methods for a diiusion problem with nonconstant ccccients. Application to a convection diiusion problem, East-West J. Numer. Math, vol.3, issue.4, pp.237-254, 1995. ,
On the existence of multiple steady-state solutions in the theory of electrodiiusion . I: The nonelectroneutral case. II: A constructive method for the electro-neutral case, Transactions of the American Mathematical Society, vol.350, issue.12, pp.4709-4756, 1998. ,
DOI : 10.1090/S0002-9947-98-02334-4
A uniqueness theorem for reverse biased diodes, Applicable Analysis, vol.52, issue.1-4, pp.262-276, 1994. ,
DOI : 10.1016/0362-546X(80)90097-8
A PHASE PLANE ANALYSIS OF TRANSONIC SOLUTIONS FOR THE HYDRODYNAMIC SEMICONDUCTOR MODEL, Mathematical Models and Methods in Applied Sciences, vol.01, issue.03, pp.347-376, 1991. ,
DOI : 10.1142/S0218202591000174
Conditioning of the Steady State Semiconductor Device Problem, SIAM Journal on Applied Mathematics, vol.49, issue.1, pp.165-185, 1989. ,
DOI : 10.1137/0149010
On Numerical Differential Algebraic Problems with Application to Semiconductor Device Simulation, SIAM Journal on Numerical Analysis, vol.26, issue.3, pp.517-538, 1989. ,
DOI : 10.1137/0726031
Numerical Methods for Semiconductor Device Simulation, SIAM Journal on Scientific and Statistical Computing, vol.4, issue.3, pp.416-435, 1983. ,
DOI : 10.1137/0904032
Analytical and numerical aspects of semiconductor device modeling, pp.82-11274, 1982. ,
EEet de la temp erature de r eseau dans l'analyse et la simulation des semiconducteurs, Th ese de l'universit e de Reims, 1998. ,
Introduction to nite and boundary element methods for engineers, 1992. ,
Hierarchical PDE simulation of nonequilibrium transport eeects in semiconductors devices, NUPAD IV, pp.155-160, 1992. ,
Transport equations for electrons in two-valley semiconductors, IEEE Transactions on Electron Devices, vol.17, issue.1, pp.38-47, 1970. ,
DOI : 10.1109/T-ED.1970.16921
On some numerical problems in semiconductor device simulation, Lect. Notes Math, vol.78, issue.2, pp.31-42, 1991. ,
DOI : 10.1016/0021-9991(88)90053-8
Two-Dimensional Exponential Fitting and Applications to Drift-Diffusion Models, SIAM Journal on Numerical Analysis, vol.26, issue.6, pp.1342-1355, 1989. ,
DOI : 10.1137/0726078
A Singular Perturbation Analysis of Reverse-Biased Semiconductor Diodes, SIAM Journal on Mathematical Analysis, vol.20, issue.2, pp.372-387, 1989. ,
DOI : 10.1137/0520024
Mixed and hybrid nite element methods, Series in computational Mathematics, 1991. ,
Mathematical properties of one-dimensional semiconductors, Mat. Apl. Comp, vol.5, pp.123-137, 1986. ,
Theoretical and numerical problems in reverse biased semiconductor device, Computing methods in applied sciences and engineering VII, pp.45-58, 1986. ,
A New Method of Solving Nonlinear Simultaneous Equations, The Computer Journal, vol.12, issue.1, pp.94-99, 1969. ,
DOI : 10.1093/comjnl/12.1.94
Modeling and Analysis of Laser-Beam-Induced Current Images in Semiconductors, SIAM Journal on Applied Mathematics, vol.53, issue.1, pp.187-204, 1993. ,
DOI : 10.1137/0153012
A singular perturbation problem for semiconductors, Bolletino U.M.I, vol.1, issue.7, pp.409-421, 1987. ,
Finite Element Analysis of the One-Dimensional Full Drift-Diffusion Semiconductor Model, SIAM Journal on Numerical Analysis, vol.32, issue.2, pp.455-483, 1995. ,
DOI : 10.1137/0732019
On the existence of a solution in a domain identification problem, Journal of Mathematical Analysis and Applications, vol.52, issue.2, pp.189-289, 1975. ,
DOI : 10.1016/0022-247X(75)90091-8
The nite element method for elliptic problems, 1986. ,
Two-Dimensional numerical simulation of energie transport eeect in Si and GaAs MESFET's, IEEE Trans. El. DEv, issue.6, pp.29-970, 1982. ,
Diierential equations, Marcel Dekker, 1980. ,
An accurate Numerical steady-state one-dimensional solution of the P-N Junction , Solid-State Electron, pp.33-58, 1968. ,
An accurate numerical one-dimensional solution of the p-n junction under arbitrary transient conditions, Solid-State Electronics, vol.11, issue.11, pp.1021-2053, 1968. ,
DOI : 10.1016/0038-1101(68)90126-3
A steady state potential flow model for semiconductors, Annali di Matematica Pura ed Applicata, vol.165, issue.1, pp.87-98, 1993. ,
DOI : 10.1007/BF01765842
Uniform numerical methods for problems with initial and boundary layers, 1980. ,
Accelerating with rank-one updates, Lin. Alg. and its appl, pp.511-520, 1989. ,
Arclength continuation methods and applications to 2D drift-diiusion semiconductor equations, pp.36-47, 1996. ,
Mixed nite element approach and nonlinear implicit schemes for drift-diiusion equation solution of 2D heterojunction semiconductor devices, Compel, pp.609-640, 1994. ,
On the numerical solution of a free boundary identiication problem, Dynamic systems identiication and inverse problems, pp.135-143, 1998. ,
statistics of electrons and applications to devices, in solid state theory, P.T.Landsberg, pp.256-324, 1969. ,
On the stationary semiconductor equations arising in modeling an LBIC technique, Applied Mathematics & Optimization, vol.51, issue.2, pp.189-202, 1996. ,
DOI : 10.1007/BF01183143
Solution of the hydrodynamic device model using high-order nonoscillatory shock capturing algorithms, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol.10, issue.2, pp.232-244, 1991. ,
DOI : 10.1109/43.68410
A second-order L-stable time discretisation of the semiconductor device equations, Journal of Computational and Applied Mathematics, vol.42, issue.2, pp.175-186, 1992. ,
DOI : 10.1016/0377-0427(92)90072-6
On existence of weak solutions to a system of stationary semiconductor equations with avalanche generation, M3AS, pp.273-289, 1994. ,
A Course in Solving Real-World Problems, SIAM, 1994. ,
An interpretation of the Scharfetter-Gummel schemme as a mixed nite element discretization, Rep. Akad. Wiss. DDR, Karl-Weierstrass-Inst. Math, vol.3, pp.1-7, 1990. ,
On uniqueness and stability of steady-state carrier distributions in semiconductors, Lect. Notes Math, vol.4, pp.209-214, 1986. ,
DOI : 10.1016/0362-546X(80)90097-8
On Existence, Uniqueness and Asymptotic Behavior of Solutions of the Basic Equations for Carrier Transport in Semiconductors, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.294, issue.2, pp.101-108, 1985. ,
DOI : 10.1002/zamm.19850650210
Stationary transonic solutions of a one-dimensional hydrodynamic model for semiconductors, Commun. Partial Diier. Equations, vol.174, issue.3, pp.553-577, 1992. ,
Boundary???layer formation for viscosity approximations in transonic flow, Physics of Fluids A: Fluid Dynamics, vol.4, issue.3, pp.486-490, 1992. ,
DOI : 10.1063/1.858321
Shock Waves in the Hydrodynamic Model for Semiconductor Devices, Math. Appl, vol.59, pp.123-134, 1994. ,
DOI : 10.1007/978-1-4613-8410-6_7
Elliptic partial equations of second order, 1977. ,
Analyse num erique des in equations variationnelles, M ethodes Math ematiques de l, 1976. ,
Elliptic problems in nonsmooth domains, Monographs and studies in Mathematics, 1985. ,
AW 1,p -estimate for solutions to mixed boundary value problems for second order elliptic differential equations, Mathematische Annalen, vol.9, issue.4, pp.679-687, 1989. ,
DOI : 10.1007/BF01442860
On the Boundedness of Solutions to the Basic Equations in Semiconductor Theory, Mathematische Nachrichten, vol.29, issue.1, pp.167-174, 1986. ,
DOI : 10.1002/mana.19861290115
Finite element approximation for optimal shape, material and topology design, 1996. ,
Existence and Regularity for Van-Roosbroek systems with general mixed boundary conditions, Compel, pp.217-228, 1990. ,
On a Variational Inequality and Its Approximation, in the Theory of Semiconductors, SIAM Journal on Numerical Analysis, vol.12, issue.6, pp.938-950, 1975. ,
DOI : 10.1137/0712069
In equations variationnelles et d etermination de la charge d'espace de certains semi-conducteurs, pp.1409-1412, 1974. ,
Analysis of charge transport. A Mathematical study of semiconductor devices, 1995. ,
Consistency of Semiconductor Modeling: An Existence/Stability Analysis for the Stationary Van Roosbroeck System, SIAM Journal on Applied Mathematics, vol.45, issue.4, pp.565-590, 1985. ,
DOI : 10.1137/0145034
Energy Models for One-Carrier Transport in Semiconductor Devices, Math. Appl, vol.59, pp.185-207, 1994. ,
DOI : 10.1007/978-1-4613-8410-6_10
Simulation of MESFET device by streamline-diiusion nite element methods, pp.5-20, 1996. ,
A STREAMLINE-UPWINDING/PETROV-GALERKIN METHOD FOR THE HYDRODYNAMIC SEMICONDUCTOR DEVICE MODEL, Mathematical Models and Methods in Applied Sciences, vol.05, issue.05, pp.659-681, 1995. ,
DOI : 10.1142/S0218202595000383
Intoduction a la th eorie des points critiques et applications aux probl emes elliptiques, 1993. ,
A Proof of Convergence of Gummel???s Algorithm for Realistic Device Geometries, SIAM Journal on Numerical Analysis, vol.23, issue.6, pp.1121-1137, 1986. ,
DOI : 10.1137/0723076
The moments of the Boltzmann transport equation as applied to the Gallium arsenide permiable base transistor, pp.99-105, 1987. ,
Numerical analysis for semiconductor devices, 1982. ,
Effect of mesh spacing on static negative resistance in GaAs MESFET simulation, IEEE Transactions on Electron Devices, vol.28, issue.1, pp.120-122, 1981. ,
DOI : 10.1109/T-ED.1981.20293
Advanced semiconductor device physics and modeling, Artechouse, 1994. ,
On basic semiconductor equations with heat conduction, J. Partial Diier. Equations, vol.8, issue.1, pp.43-54, 1995. ,
A non-isentropic Euler-Poisson model for a collisionless plasma, Mathematical Methods in the Applied Sciences, vol.3, issue.6, pp.409-442, 1993. ,
DOI : 10.1002/mma.1670160603
Stability of the Linearized Transient Semiconductor Device Equations, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.29, issue.7, pp.319-332, 1987. ,
DOI : 10.1002/zamm.19870670710
the stationary semiconductor device equations, 1986. ,
A Nonlinear Eigenvalue Problem Modelling the Avalanche Effect in Semiconductor Diodes, SIAM Journal on Mathematical Analysis, vol.16, issue.6, pp.1268-1283, 1985. ,
DOI : 10.1137/0516091
An asymptotic Analysis of singlejunction semiconductor devices, 1983. ,
A Singularly Perturbed Boundary Value Problem Modelling a Semiconductor Device, SIAM Journal on Applied Mathematics, vol.44, issue.2, 1982. ,
DOI : 10.1137/0144018
Simulation of energy transport models via mixed nite elements, pp.535-541, 1996. ,
Physique des semi-conducteurs et des composants electroniques, 1980. ,
A Tetrahedral Mixed Finite Element Method for the Stationary Semiconductor Continuity Equations, SIAM Journal on Numerical Analysis, vol.31, issue.1, pp.196-216, 1994. ,
DOI : 10.1137/0731010
Analysis of mathematical models of semiconductor devices, Boole Press advances in numerical computation series, 1983. ,
AN EXAMPLE OF NONUNIQUENESS OF STATIONARY SOLUTIONS IN SEMICONDUCTOR DEVICE MODELS, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.1, issue.3, pp.165-174, 1982. ,
DOI : 10.1108/eb009970
Asymptotic behavior of solutions of transport equations for semiconductor devices, Journal of Mathematical Analysis and Applications, vol.49, issue.1, pp.215-255, 1975. ,
DOI : 10.1016/0022-247X(75)90172-9
An Initial Value Problem from Semiconductor Device Theory, SIAM Journal on Mathematical Analysis, vol.5, issue.4, pp.597-612, 1974. ,
DOI : 10.1137/0505061
On equations describing steady-state carrier distributions in a semiconductor device, Communications on Pure and Applied Mathematics, vol.11, issue.6, pp.781-792, 1972. ,
DOI : 10.1002/cpa.3160250606
Iterative solution of the drift-diiusion equations, Numerical Algorithms, pp.323-342, 1999. ,
Solution it erative d'un probl eme mixte pour le potentiel electrostatique dans les semi-conducteurs, Lebanese scientiic research reports, pp.307-321, 1998. ,
Sufficient Conditions for Converging Drift-Diffusion Discrete Systems. Application to The Finite Element Method, Mathematical Methods in the Applied Sciences, vol.3, issue.1, pp.33-51, 1996. ,
DOI : 10.1002/(SICI)1099-1476(19960110)19:1<33::AID-MMA759>3.0.CO;2-H
On the uniqueness of the solution to the drift-diiusion model in semiconductor analysis, Compel, vol.2, issue.3, pp.377-390, 1992. ,
Une m ethode d' el ements nis hybrides pour une in equation quasi-varitionnelle mod elisant un semi-conducteur, Proceeding of the rst applied mathematical's days, E.M.I, vol.1, pp.352-357, 1992. ,
Contribution a l'analyse et l'approximation des mod eles d erive-diiusion dans les semi-conducteurs, Th ese de Doctorat, 1991. ,
Les m ethodes directes en th eorie des equations elliptiques, 1967. ,
Analyse num erique des equations stationnaires des semi-conducteurs r esolution par el ements nis mixtes, 1989. ,
Semiconductor device modelling from the numerical point of view, International Journal for Numerical Methods in Engineering, vol.2, issue.4, pp.763-838, 1987. ,
DOI : 10.1002/nme.1620240408
Computation of drain and substate currents in ultra-short-channel NMOSFET's using the hydrodynamic model, pp.115-119, 1991. ,
Electro-diiusion of ions, SIAM Studies in Applied Mathematics, 1990. ,
Multi-dimensional discretization scheme for the hydrodynamic model of semiconductor devices, Compel, pp.149-183, 1986. ,
Mixed finite volume methods for semiconductor device simulation, Numerical Methods for Partial Differential Equations, vol.13, issue.3, pp.215-236, 1997. ,
DOI : 10.1002/(SICI)1098-2426(199705)13:3<215::AID-NUM1>3.0.CO;2-Q
Physics of semiconductors, 1995. ,
DOI : 10.1007/978-1-4612-4168-3
Large-signal analysis of a silicon Read diode oscillator, IEEE Transactions on Electron Devices, vol.16, issue.1, pp.64-144, 1969. ,
DOI : 10.1109/T-ED.1969.16566
A Singular Perturbation Analysis of Reverse Biased $pn$-Junctions, SIAM Journal on Mathematical Analysis, vol.21, issue.2, pp.313-326, 1990. ,
DOI : 10.1137/0521017
Analysis of breakdown phenomena in MOSFET's, IEEE Trans. Computer-Aided-Design of integrated circuits, pp.77-85, 1982. ,
Time dependent solution of a nonlinear system arising in semiconductor theory, II Boundedness and perioidicity, Nonlinear Analysis, pp.491-502, 1986. ,
Time-dependent solutions of a nonlinear system arising in semiconductor theory, Nonlinear Analysis: Theory, Methods & Applications, vol.9, issue.11, pp.1137-1157, 1985. ,
DOI : 10.1016/0362-546X(85)90026-4
Steady state solutions of diiusion-reaction systems with electrostatic convection, Nonlinear Analysis, Theory Methods Appl, vol.4, issue.1, pp.52-64, 1984. ,
Analysis and simulation of semiconductor devices, 1984. ,
DOI : 10.1007/978-3-7091-8752-4
DELAUNAY PARTITIONING IN THREE DIMENSIONS AND SEMICONDUCTOR MODELS, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.5, issue.2, pp.75-93, 1986. ,
DOI : 10.1108/eb010019
Les transistors a eeet de champs, 1967. ,
Semiconductor device modeling using ux upwinding nite elements, Compel, vol.8, issue.4, pp.219-224, 1989. ,
Some aspects of semiconductor device simulation, In computing methods in applied sciences and engineering VII, pp.3-12, 1986. ,
Hilbert Space Methods for Partial Diierential Equations, 1979. ,
Introducton to numerical analysis, 1980. ,
Comparative studies of hydrodynamic and energy transport models, Compel, pp.439-453, 1994. ,
A Bifurcation Analysis of the One-Dimensional Steady-State Semiconductor Device Equations, SIAM Journal on Applied Mathematics, vol.49, issue.4, pp.1102-1121, 1989. ,
DOI : 10.1137/0149066
An analysis of the nite element method, NJ, 1973. ,
Physique des mat eriaux conducteurs et semi-conducteurs, 1992. ,
elliptic diierential equations and obstacle problems, 1987. ,
Theory of ow of electrons and holes in germanium and other semiconductors , Bell System Tech, J, vol.29, pp.560-607, 1950. ,
Singularly perturbed equations in the critical case, 1978. ,
Singularly Disturbed systems of the theory of semiconductor devices, Math. Fiz, vol.17, issue.2, pp.339-348, 1977. ,
On uniqueness for the stationary semiconductor devices, pp.217-232, 1995. ,
CONNECTING WAVEFORM RELAXATION CONVERGENCE PROPERTIES TO THE A??? STABILITY OF MULTIRATE INTEGRATION METHODS, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.10, issue.4, pp.497-508, 1991. ,
DOI : 10.1108/eb051724
ON THE STABILITY OF TIME DISCRETISATIONS FOR THE SEMICONDUCTOR EQUATIONS, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol.10, issue.1, pp.11-25, 1991. ,
DOI : 10.1108/eb010327