Amorphous Polymers and Non-Newtonian Fluids by R. Byron Bird (auth.), Constantine Dafermos, J. L. Ericksen,

By R. Byron Bird (auth.), Constantine Dafermos, J. L. Ericksen, David Kinderlehrer (eds.)

This IMA quantity in arithmetic and its functions AMORPHOUS POLYMERS AND NON-NEWTONIAN FLUIDS is partially the complaints of a workshop which used to be an essential component of the 1984-85 IMA software on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS we're thankful to the medical Committee: Haim Brezis Constantine Dafermos Jerry Ericksen David Kinderlehrer for making plans and imposing an exhilarating and stimulating year-long application. We espe­ cially thank this system Organizers, Jerry Ericksen, David Kinderlehrer, Stephen Prager and Matthew Tirrell for organizing a workshop which introduced jointly scientists and mathematicians in various parts for a fruitful alternate of principles. George R. promote Hans Weinberger Preface studies with amorphous polymers have provided a lot of the inducement for constructing novel different types of molecular idea, to attempt to accommodate the extra major beneficial properties of platforms related to very huge molecules with many levels offreedom. equally, the observations of many strange macroscopic phenomena has motivated efforts to strengthen linear and nonlinear theories of viscoelasticity to explain them. In both occasion, we're faced no longer with a well-established, particular set of equations, yet with numerous equations, conforming to a unfastened development and steered via common forms of reasoning. One problem is to plot options for locating equations in a position to providing certain and trustworthy predictions. on the topic of this can be the problem of learning how one can larger snatch the character of recommendations ofthose equations exhibiting a few promise.

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T. J. R. Hughes and T. E. Tezduyar, "Finite element methods for first-order hyperbolic sysems with particular emphasis on the compressible Euler equations", Comp. Meth. Appl. Mech. , 4S, 217 (1984). 14. J. W. Barrett, K. W. Morton, "Approximate symmetrization and Petrov-Galerkin methods for diffusion-convection problems", Comp. Meth. Appl. Mech. , 4S, 97 (1984). 15. F. C. Bisshopp, Private Communication. 16. O. Hasseger and C. Bisgaard, "A Lagrangian finite element method for the flow of non-Newtonian liquids", J.

Fluid f10w problems and their associated transport problems are notorious for the convergence barriers which appear when the governing equations become domina ted by convective terms which are responsible for the loss of self -adjointness. Closely connected with these features is the possibility of change of type as the controlling parameter is varied. For the convection-diffusion equation the purely convective case re duces the system to first order hyperbolic. The results of recent investigations of Joseph [11] on the viscoelastic f10ws associated with several constitutive equations show some remarkable analogies to the transonic f10w problem for the case when inertia is a significant parameter.

T) may blow up to infinity uo. and the kernel K(t) satisfy appropriate conditions. the effect of memory is dissipative and. as a result. 1). 3). 4). 2) exist globally in time. providing uo(x) is smooth and "smalI" (cf. [17. 3. 21]). Unfortunately. the damping induced by fading memory is weak and so smooth solutions break down in finite time when uo(x) is "Iarge" (cf. [16. 3. 21]). 1). 3). 4). 2) in the class of locally bounded measurable functions. under bounded measurable initial data. has been established in [5].

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