Two　different　systems　which　can　be　regard　as　the　extreme　cases　of　Landau-Lifshitz-Gilbert　equation　are　considered.　When　the　gyromagnetic　term　of　Landau-Lifshitz-Gilbert　equation　vanishes　away,　we　consider　some　special　solutions　for　a　modified　harmonic　map　heat　flow　which　map　from　(2　+　1)-dimensional　space-time　into　the　2-sphere.　The　existence　of　regular　initial　data　leading　to　blow　up　in　finite　time　is　established.　When　the　Gilbert　term　is　omitted,　a　blowup　solution　is　obtained　by　constructing　a　blowup　solution　of　Landau-Lifshitz　equation.　(C)　2012　Elsevier　Inc.　All　rights　reserved.