Pointwise bounds and blow-up for nonlinear fractional parabolic inequalities Academic Article uri icon

abstract

  • 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.

published proceedings

  • JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES

author list (cited authors)

  • Taliaferro, S. D.

citation count

  • 4

complete list of authors

  • Taliaferro, Steven D

publication date

  • January 2020