On Abstract Volterra Equations with Kernels Having a Positive Resolvent.
Abstract
The nonlinear abstract Volterra equation of convolution type is considered. Boundedness and asymptotic properties of the solutions are established under the assumption that the kernel satisfies certain natural positivity conditions. An important property of linear and nonlinear diffusion equations is that the solutions of such equations obey a 'maximum principle'. In particular, if the initial data and the forcing terms are nonnegative, then the solution is nonnegative. The Volterra equation (V) is an abstraction of a mathematical model for nonlinear heat flow in a material with 'memory'. The kernel b in (V) can be expressed in terms of the physically meaningful heat flux and internal energy relaxation functions. In this paper equation (V) for a class of kernels b is considered which insure the positivity of the solution operator.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1979
- Accession Number
- ADA077124
Entities
People
- Ph. Clement
Organizations
- University of Wisconsin–Madison