摘要
This paper deals with the Cauchy problem for a doubly singular parabolic equation with a weighted source ut=div｜u｜p-2um）＋｜x｜α uq ,（x,t）∈RN×（0,t）,where N ≥ 1, 1 〈 p 〈 2, m 〉 max（0,3 -p/N} satisfying 2 〈 p＋m 〈 3, q 〉 1, and（α 〉 N（3 - p - m） - p. We give the secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and non-existence of global solutions of the Cauchy problem. Moreover, the life span of solutions is also studied.
This paper deals with the Cauchy problem for a doubly singular parabolic equation with a weighted source ut=div｜u｜p-2um）＋｜x｜α uq ,（x,t）∈RN×（0,t）,where N ≥ 1, 1 〈 p 〈 2, m 〉 max（0,3 -p/N} satisfying 2 〈 p＋m 〈 3, q 〉 1, and（α 〉 N（3 - p - m） - p. We give the secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and non-existence of global solutions of the Cauchy problem. Moreover, the life span of solutions is also studied.
基金
partially supported by the Doctor Start-up Funding and Natural Science Foundation of Chongqing University of Posts and Telecommunications(A2014-25 and A2014-106)
partially supported by Scientific and Technological Research Program of Chongqing Municipal Education Commission(KJ1500403)
the Basic and Advanced Research Project of CQCSTC(cstc2015jcyj A00008)
partially supported by NSFC(11371384),partially supported by NSFC(11426047)
the Basic and Advanced Research Project of CQCSTC(cstc2014jcyj A00040)
the Research Fund of Chongqing Technology and Business University(2014-56-11)
