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  • Bubnov-Galerkin approximations  (1)
  • Chemistry  (1)
  • ELECTRONICS AND ELECTRICAL ENGINEERING
  • 1995-1999  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of dynamics and differential equations 9 (1997), S. 373-400 
    ISSN: 1572-9222
    Keywords: Inertial manifolds ; exponential attractors ; approximate inertial manifolds ; Bubnov-Galerkin approximations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Suppose that the family of evolution equationsdu/dt+Au+f N (u)=0 possesses inertial manifolds of the same dimension for a sequence of nonlinear termsf N withf N →f in the C0 norm. Conditions are found to ensure that the limiting equationdu/dt+Au+f(u)=0 also possesses an inertial manifold. There are two cases. The first, where the manifolds for the family have a bounded Lipschitz constant, is straightforward and leads to an interesting result on inertial manifolds for Bubnov-Galerkin approximations. When the Lipschitz constant is unbounded, it is still possible to prove the existence of an exponential attractor of finite Hausdorff dimension for the limiting equation. This more general result is applied to a problem in approximate inertial manifold theory discussed by Sell (1993).
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 0006-3592
    Keywords: methanol sensor ; methanol monitoring and control ; methylotrophic yeast fermentation ; Pichia pastoris ; transferrin ; shake-flask cultures ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The methylotrophic yeast Pichia pastoris can be used to express recombinant genes at high levels under the control of the methanol-inducible alcohol oxidase 1 (AOX1) promoter. Accurate regulation of the methanol concentration in P. pastoris cultures is necessary to maintain induction, while preventing accumulation of methanol to cytotoxic levels. We developed an inexpensive methanol sensor that uses a gas-permeable silicone rubber tube immersed in the culture medium and an organic solvent vapor detector. The sensor was used to monitor methanol concentration continuously throughout a fed-batch shake-flask culture of a P. pastoris clone producing the N-lobe of human transferrin. The sensor calibration was stable for the duration of the culture and the output signal accurately reflected the methanol concentration determined off-line by HPLC. A closed-loop control system utilizing this sensor was developed and used to maintain a 0.3% (v/v) methanol concentration in the culture. Use of this system resulted in a fivefold increase in volumetric protein productivity over levels obtained using the conventional fed-batch protocol. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 279-286, 1997.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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