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Degenerate Diffusions by Stuart S. Antman, Massimo Lanza De Cristoforis (auth.),

By Stuart S. Antman, Massimo Lanza De Cristoforis (auth.), Wei-Ming Ni, L. A. Peletier, J. L. Vazquez (eds.)

This quantity is the court cases of the IMA workshop "Degenerate Diffusions" held on the college of Minnesota from could 13-May 18, 1991. The workshop consisted of 2 components. The emphasis of the 1st 4 days was once on present development or new difficulties in nonlinear diffusions related to unfastened limitations or sharp interfaces. Analysts and geometers will locate many of the mathematical types defined during this quantity attention-grabbing; and the papers of extra natural mathematical nature incorporated the following should still supply utilized mathematicians with strong equipment and beneficial ideas in dealing with singular perturbation difficulties in addition to loose boundary difficulties. The final days of the workshop have been a party of James Serrin's sixty fifth birthday. a variety of issues was once lined during this a part of the workshop. for that reason, the scope of this e-book is far broader than what the identify Degenerate Diffusions may perhaps recommend.

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We follow the asymptotic analysis of §3 using the same notation and making the same assumptions. u - ~ 71 ,,2 f "( - u) >- O. O(t) + OCE), which are valid for all x E n \ roc t) and t E [0, T]. 8b) A simple calculation yields that ° u (x) = uO = ±1 and {I, x E n~(t) := {x En: UO(x, t) > O}, ° ° where -1, x E n_(t):= {x En: u (x,t) < O}, ° In+1 = (lnl + m)/2. 9) € which stretches the transition layer, and write the inner expansion in terms of the (y, s) coordinate system. f. 10) nn and r~ := an~ n n.

M. LANZA DE CRISTOFORIS, Cavitational flows and global injectivity of conformal maps, Trans. Amer. Math. , 323 (1991), pp. 509-527. , The large deformation of nonlinearly elastic rings in a two-dimensional compressible flow, (to appear). M. LANZA DE CRISTOFORIS & S. S. ANTMAN, Cavitational flow past a nonlinearly elastic panel, Indiana Univ. Math. , 39 (1990), pp. 383-412. , The large deformation of elastic tubes in two-dimensional flows, SIAM J. Math. , 22 (1991), pp. 1193-122l. , The large deformation of nonlinearly elastic shells in axisymmetric flows, Analyse nonlineaire ( to appear).

T = €2/4. 704. 2, one may show that when lu(x, t)1 < 1 u(x,t) = I~I 00 + Lll'j(0)exp(1/. x = -m/(€Inl). All but a finite number of modes in the expansion decay away. 1 for n = 50,100, ... ,850. During the early stages there are several "blobs" which appear and then quickly disappear. The motion of the €-interfacial region is towards a strip approximating a line, being the minimal interface dividing n into two equal measure sets. t) quickly moves towards the shape of a quarter circle, which for this value of m approximates the minimal interface.

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