id sid tid token lemma pos g732d794052 1 1 we we PRON g732d794052 1 2 study study VERB g732d794052 1 3 the the DET g732d794052 1 4 blowup blowup NOUN g732d794052 1 5 problem problem NOUN g732d794052 1 6 for for ADP g732d794052 1 7 nonlinear nonlinear ADJ g732d794052 1 8 heat heat NOUN g732d794052 1 9 equations equation NOUN g732d794052 1 10 . . PUNCT g732d794052 2 1 we we PRON g732d794052 2 2 show show VERB g732d794052 2 3 that that SCONJ g732d794052 2 4 if if SCONJ g732d794052 2 5 the the DET g732d794052 2 6 even even ADJ g732d794052 2 7 initial initial ADJ g732d794052 2 8 value value NOUN g732d794052 2 9 is be AUX g732d794052 2 10 close close ADJ g732d794052 2 11 enough enough ADV g732d794052 2 12 to to ADP g732d794052 2 13 a a DET g732d794052 2 14 2 2 NUM g732d794052 2 15 - - PUNCT g732d794052 2 16 dimensional dimensional ADJ g732d794052 2 17 manifold manifold NOUN g732d794052 2 18 of of ADP g732d794052 2 19 approximately approximately ADV g732d794052 2 20 homogenous homogenous ADJ g732d794052 2 21 solutions solution NOUN g732d794052 2 22 , , PUNCT g732d794052 2 23 the the DET g732d794052 2 24 solution solution NOUN g732d794052 2 25 blows blow VERB g732d794052 2 26 up up ADP g732d794052 2 27 in in ADP g732d794052 2 28 a a DET g732d794052 2 29 finite finite ADJ g732d794052 2 30 time time NOUN g732d794052 2 31 and and CCONJ g732d794052 2 32 the the DET g732d794052 2 33 asymptotical asymptotical ADJ g732d794052 2 34 profile profile NOUN g732d794052 2 35 is be AUX g732d794052 2 36 an an DET g732d794052 2 37 approximate approximate ADJ g732d794052 2 38 solution solution NOUN g732d794052 2 39 with with ADP g732d794052 2 40 parameters parameter NOUN g732d794052 2 41 evolving evolve VERB g732d794052 2 42 according accord VERB g732d794052 2 43 to to ADP g732d794052 2 44 a a DET g732d794052 2 45 certain certain ADJ g732d794052 2 46 dynamical dynamical ADJ g732d794052 2 47 system system NOUN g732d794052 2 48 plus plus CCONJ g732d794052 2 49 a a DET g732d794052 2 50 small small ADJ g732d794052 2 51 fluctuation fluctuation NOUN g732d794052 2 52 in in ADP g732d794052 2 53 $ $ SYM g732d794052 2 54 l^infty$.the l^infty$.the PRON g732d794052 2 55 result result NOUN g732d794052 2 56 allows allow VERB g732d794052 2 57 us we PRON g732d794052 2 58 to to PART g732d794052 2 59 construct construct VERB g732d794052 2 60 initial initial ADJ g732d794052 2 61 data datum NOUN g732d794052 2 62 with with ADP g732d794052 2 63 more more ADJ g732d794052 2 64 than than ADP g732d794052 2 65 one one NUM g732d794052 2 66 local local ADJ g732d794052 2 67 maximum maximum NOUN g732d794052 2 68 while while SCONJ g732d794052 2 69 the the DET g732d794052 2 70 solutions solution NOUN g732d794052 2 71 still still ADV g732d794052 2 72 blow blow VERB g732d794052 2 73 up up ADP g732d794052 2 74 in in ADP g732d794052 2 75 a a DET g732d794052 2 76 finite finite ADJ g732d794052 2 77 time time NOUN g732d794052 2 78 according accord VERB g732d794052 2 79 to to ADP g732d794052 2 80 the the DET g732d794052 2 81 asymptotical asymptotical ADJ g732d794052 2 82 profile profile NOUN g732d794052 2 83 . . PUNCT g732d794052 3 1 we we PRON g732d794052 3 2 also also ADV g732d794052 3 3 demonstrated demonstrate VERB g732d794052 3 4 that that SCONJ g732d794052 3 5 there there PRON g732d794052 3 6 is be VERB g732d794052 3 7 an an DET g732d794052 3 8 open open ADJ g732d794052 3 9 subset subset NOUN g732d794052 3 10 in in ADP g732d794052 3 11 the the DET g732d794052 3 12 space space NOUN g732d794052 3 13 of of ADP g732d794052 3 14 initial initial ADJ g732d794052 3 15 data datum NOUN g732d794052 3 16 and and CCONJ g732d794052 3 17 their their PRON g732d794052 3 18 solutions solution NOUN g732d794052 3 19 blow blow VERB g732d794052 3 20 up up ADP g732d794052 3 21 according accord VERB g732d794052 3 22 to to ADP g732d794052 3 23 the the DET g732d794052 3 24 described describe VERB g732d794052 3 25 asymptotical asymptotical ADJ g732d794052 3 26 profile profile NOUN g732d794052 3 27 . . PUNCT