Pointwise bounds and blow-up for nonlinear fractional parabolic inequalities

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.

authors

• Taliaferro, Steven

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

publisher

• Elsevier  Publisher

published in

• JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES  Journal

keywords

• Blow-up
• Fractional Heat Operator
• Parabolic
• Pointwise Bounds

Digital Object Identifier (DOI)

• 10.1016/j.matpur.2019.05.012

start page

• 287

end page

• 328

volume

• 133

URL

• http://dx.doi.org/10.1016/j.matpur.2019.05.012