| Academic Article individual record

2019 Elsevier Masson SAS We investigate pointwise upper bounds for nonnegative solutions u(x,t) of the nonlinear initial value problem 0( t ) uu in R n R,n1, u=0in R n (,0) where and are positive constants. To do this we first give a definitiontailored for our study of (0.1), (0.2)of fractional powers of the heat operator ( t ) :YX where X and Y are linear spaces whose elements are real valued functions on R n R and 0<< 0 for some 0 which depends on n, X and Y. We then obtain, when they exist, optimal pointwise upper bounds on R n (0,) for nonnegative solutions uY of the initial value problem (0.1), (0.2) with particular emphasis on those bounds as t0 + and as t.

publication outlet

Journal de Mathmatiques Pures et Appliques

author list (cited authors)
Taliaferro, S. D.
publication date
Elsevier bv Publisher
  • Pointwise Bounds
  • Parabolic
  • Fractional Heat Operator
  • Blow-up
Digital Object Identifier (DOI)