Geodesic
On the global unsolvability of Cauchy problems for quasilinear parabolic equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 5, pp. 1072-1087

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Sufficient conditions are found for global unsolvability of the Cauchy problem for parabolic equations of the non-linear heat conduction type with a source. In the case of equations of a special kind, the class of initial functions is isolated, with which the Cauchy problem is globally solvable. 
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     author = {V. A. Galaktionov},
     title = {On the global unsolvability of {Cauchy} problems for quasilinear parabolic equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1072--1087},
     publisher = {mathdoc},
     volume = {23},
     number = {5},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_5_a4/}
}
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V. A. Galaktionov. On the global unsolvability of Cauchy problems for quasilinear parabolic equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 5, pp. 1072-1087. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_5_a4/