Accession Number : AD0730017

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

Corporate Author : BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

Personal Author(s) : Chafee,N. ; Infante,E. F.

Report Date : 1971

Pagination or Media Count : 37

Abstract : The document discusses the boundary value problem (upsilon) where u(supt) = u(sup xx) + lambda f(u), (0 < or = x < or = pi, 0 < t < positive infinite); u(x=0) = u(x= pi) = 0, (0 < or = t < positive infinity); u(t=0) = phi(x), (0 < or = x < or = pi). Here, lambda is a non-negative parameter; f is a given real-valued function defined and of class c(sup 2) on (-infinity, + infinity); and phi is an arbitrarily specified function of class C(sup 1) on (0, pi) satisfying phi(0) = phi(pi) = 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 :   (*NONLINEAR DIFFERENTIAL EQUATIONS, INTEGRATION), (*PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS), BANACH SPACE, MAPPING(TRANSFORMATIONS), SET THEORY, TOPOLOGY, ITERATIONS, STABILITY, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE