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Sur un système d’E.D.P. modélisant un processus d’adsorption isotherme d’un mélange gazeux. (On a system of P.D.E. modelling isothermal adsorption of a gaseous mixture). (French. English summary) Zbl 0765.76092

Summary: We present a study of a nonlinear system of hyperbolic P.D.E. used as a model in chemical engineering. We obtain an existence and uniqueness result when the initial data have bounded variation, then an existence result with initial data in \(L^ \infty\). Lastly, within a simplified model, we study the solutions corresponding to a sequence of initial data that converges weakly in \(L^ \infty\): making use of a counterexample, we show that there is generally no weak convergence to a solution of the system.

MSC:

76V05 Reaction effects in flows
35L60 First-order nonlinear hyperbolic equations
35Q35 PDEs in connection with fluid mechanics
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[1] C. BOURDARIAS, Travail en préparation.
[2] E. CANON, et F. JAMES, Résolution du problème de Cauchy pour certains systèmes hyperboliques intervenant en génie chimique (1990).
[3] [3] R. J. DIPERNA et P. L. LIONS, Ordinary differential equation transpot theory and sobolev spaces. Invent. Math. 98 (1989), p. 511-547. Zbl0696.34049 MR1022305 · Zbl 0696.34049 · doi:10.1007/BF01393835
[4] F. JAMES, Sur la modélisation mathématique des équilibres diphasiques et des colonnes de chromatographie. Thèse, École Polytechnique, nov. 1990.
[5] S. N. KRUZKOV, First order quasilinear equations in several independant variables. Math URSS Sb., vol. 10, 1970, p. 217-243. Zbl0215.16203 · Zbl 0215.16203 · doi:10.1070/SM1970v010n02ABEH002156
[6] P. L. LIONS, B. PERTHAME et E. TADMOR, Note aux C. R. Acad. Sci. Paris, sér. 1, t. 312, janv. 1991, p. 97. MR1086510
[7] H. RHEE, R. ARIS and N. R. AMUNDSON, On the theory of multicomponent chromatography. Philos. Trans. Roy. Soc. London, A 267, 1970, p. 419-455. Zbl0233.76157 · Zbl 0233.76157 · doi:10.1098/rsta.1970.0050
[8] P. M. RUTHVEN, Principles of adsorption and adsorption processes. Wiley Interscience Publ., New York, 1984.
[9] L. TARTAR, Compensated compactness and applications to partial differential equations. In Research Notes in Mathematics, 39, Herriot-Watt. Sympos. vol. 4, Pitman Press. Boston, London (1975), p. 136-211. Zbl0437.35004 MR584398 · Zbl 0437.35004
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