The Cauchy problem for a nonhomogeneous heat equation with reaction Articles uri icon

publication date

  • February 2013

start page

  • 643

end page

  • 662

issue

  • 2

volume

  • 33

International Standard Serial Number (ISSN)

  • 1078-0947

Electronic International Standard Serial Number (EISSN)

  • 1553-5231

abstract

  • We study the behaviour of the solutions to the Cauchy problem {rho(x)ut=Deltau+up,u(x,0)=u0(x),x∈RN,t∈(0,T),x∈RN, with p>0 and a positive density rho satisfying rho(x)∼|x|−sigma for large |x|, 0

keywords

  • reaction-diffusion equations; initial value problem; well-posedness; blow-up; critical exponents