# Accession Number:

## AD0730017

# Title:

## A Bifurcation Problem for a Nonlinear Partial Differential Equation of Parabolic Type,

# Descriptive Note:

# Corporate Author:

## BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

# Personal Author(s):

# Report Date:

## 1971-01-01

# Pagination or Media Count:

## 37.0

# Abstract:

The document discusses the boundary value problem upsilon where usupt usup xx lambda fu, 0 or x or pi, 0 t positive infinite ux0 ux pi 0, 0 or t positive infinity ut0 phix, 0 or x or pi. Here, lambda is a non-negative parameter f is a given real-valued function defined and of class csup 2 on -infinity, infinity and phi is an arbitrarily specified function of class Csup 1 on 0, pi satisfying phi0 phipi 0. Under suitable hypotheses concerning f, investigated is the existence and stability properties of stationary solutions for upsilon. Our approach is to interpret upsilon as a dynamical system in an appropriately chosen Banach space, and then to apply to upsilon certain known results in the theory of Liapunov stability for general dynamical systems. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics