Degenerate Diffusions

by Ni, Wei-Ming; Peletier, L. A.; Vazquez, J. L.

• ISBN13: 9780387940687
• ISBN10: 0387940685
• Format: Hardcover
• Copyright: 1993-06-01
• Publisher: Springer Verlag

Summary

This volume is the proceedings of the IMA workshop "Degenerate Diffusions" held at the University of Minnesota from May 13-May 18, 1991. The workshop consisted of two parts. The emphasis of the first four days was on current progress or new problems in nonlinear diffusions involving free boundaries or sharp interfaces. Analysts and geometers will find some of the mathematical models described in this volume interesting; and the papers of more pure mathematical nature included here should provide applied mathematicians with powerful methods and useful techniques in handling singular perturbation problems as well as free boundary problems. The last two days of the workshop were a celebration of James Serrin's 65th birthday. A wide range of topics was covered in this part of the workshop. As a consequence, the scope of this book is much broader than what the title Degenerate Diffusionsmight suggest.

Table of Contents

Foreword
Preface
Nonlinear, nonlocal problems of fluid-solid interactions	p. 1
Curvature dependent phase boundary motion and parabolic double obstacle problems	p. 19
On the Harnack inequality for non-negative solutions of singular parabolic equations	p. 61
A BMO bound for eigenfunctions on Riemannian manifolds	p. 71
On some monotonicity in time properties for a quasilinear parabolic equation with source	p. 77
On the asymptotic properties of Leray's solutions to the exterior steady three-dimensional Navier-Stokes equations with zero velocity at infinity	p. 95
Some results on blow up for semilinear parabolic problems	p. 105
Long-time behaviour of solutions of quasilinear parabolic equations	p. 127
Spike-layers in semilinear elliptic singular perturbation problems	p. 131
Evolution of nonparametric surfaces with speed depending on curvature, III. Some remarks on mean curvature and anisotropic flows	p. 141
Continuation and limit behavior for damped quasi-variational systems	p. 157
Multibump solutions of a semilinear elliptic PDE on R[superscript n]	p. 175
Einstein/Yang-Mills equations	p. 187
The Dirichlet problem for functions of least gradient	p. 197
Asymptotic behaviour of nonlinear parabolic equations. Anomalous exponents	p. 215
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