Regularizing Effects for u sub t = Delta (psi (u)).
Abstract
Nonlinear diffusion equations of the form u sub t = delta zeta (u) where zeta is a given nondecreasing function occur in many situations. Existence and uniqueness of solutions of the initial-value problem for this type of equation have been studied by many authors. The regularity of the solutions, i.e. how smooth or continuous they are, is less well understood, although many results have recently been obtained in this direction. In this paper we contribute to the study of regularity by proving estimates of the general form zeta (u) sub t > or = - c(zeta(u) + a)/t on nonnegative solutions in all of space. That is, one can bound below the time derivative of zeta(u) in a pointwise fashion by zeta (u) itself. Those results generalize those for the special case zeta(r) = r to the mth power obtained by Aronson and Benilan. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1981
- Accession Number
- ADA096673
Entities
People
- Michael G. Crandall
- Michel Pierre
Organizations
- University of Wisconsin–Madison