Blow up of the solutions of the nonlinear parabolic equation

Svetlin G. Georgiev
2009 Dynamics of Partial Differential Equations  
In this paper the Cauchy problem for nonlinear parabolic equation is investigated. We prove that the Cauchy problem has one nontrivial solution u(t, r) in the form u(t, r) = v(t)ω(r) ∈ C([0, 1)L 2 ([r 0 , ∞))) for which lim t−→1 ||u|| L 2 ([r 0 ,∞))) = ∞, where r = |x|, r 0 ≥ 1 is arbitrary chosen and fixed. Also, we prove that the solution map is not uniformly continuous. 1991 Mathematics Subject Classification. 35.
doi:10.4310/dpde.2009.v6.n1.a1 fatcat:7pywyqhweffklftr2mm2v4fp4a