摘要:

AbstractThe paper is devoted to aposterioriquantitative analysis for errors caused by linearization of non‐linear elliptic boundary value problems and their finite element realizations. We employ duality theory in convex analysis to derive computable bounds on the difference between the solution of a non‐linear problem and the solution of the linearized problem, by using the solution of the linearized problem only. We also derive computable bounds on differences between finite element solutions of the nonlinear problem and finite element solutions of the linearized problem, by using finite element solutions of the linearized problem only. Numerical experiments show that oura posteriorierror bounds are effici

ISSN:0170-4214    

DOI:10.1002/mma.1670170702

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractWe consider a two‐dimensional parabolic system with general competitive interactions as a two‐player game with conflicting objectives and with controls on the inhomogencous (source) terms. We show the existence of an optimal solution of the game as the saddle point of a suitable objective functio

ISSN:0170-4214    

DOI:10.1002/mma.1670170703

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractWe establish the best constants in the Poincaré‐type and the trace‐type inequalities for the quadratic form\documentclass{article}\pagestyle{empty}\begin{document}$ \lambda ||\,{\rm div}\,{\rm u}\,||_{L^2 }^2 \, + \,2\,\mu \,||\,\,(\nabla {\rm u}\, + \,\nabla {\rm u}^{\rm T})/2\,||_{L^2 }^2 $\end{document}which is fundamental in elasticity theory, on the space ofH1vector fieldsuon a slab vanishing on one or both of its sides. We similarly calculate those constants for the case ofH1divergence‐free vector fields. Our method, which is fairly general, has another practical application to the quadratic form ∑j,k(ajk∂ku, ∂ju)L2with coefficients ajk= akjε C inH1scalar functi

ISSN:0170-4214    

DOI:10.1002/mma.1670170704

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThe positive vertical equilibrium profiles of a phytoplankton population growing in a vertical test tube under controlled experimental conditions (temperature, salinity, light intensity at the top surface) for nutrients are discussed with reference to their stability properties for arbitrary positive initial values of the biomass concentration along the tube. Two different approaches are followed. First a stability result is established in the Sobolev normH2by estimating the norms of the perturbations recursively in successive subintervals of suitably small amplitude. The second approach provides stability in the sense of the uniform convergence as a corollary of a stability theorem for a rather general class of integro‐differential equation

ISSN:0170-4214    

DOI:10.1002/mma.1670170705

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

ISSN:0170-4214    

DOI:10.1002/mma.1670170701

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY