Geodesic
On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 457-475.

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We obtain some sufficient conditions under which solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions tend to zero or blow up in a finite time. We also give the asymptotic behavior of solutions which tend to zero as $t\rightarrow\infty$. Finally, we obtain the asymptotic behavior near the blow-up time of certain blow-up solutions and describe their blow-up set.
Classification : 35B40, 35K55, 35K60
Keywords: blow-up; global existence; asymptotic behavior; maximum principle 
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     author = {Boni, Th\'eodore K.},
     title = {On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {457--475},
     publisher = {mathdoc},
     volume = {40},
     number = {3},
     year = {1999},
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     zbl = {1011.35078},
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Boni, Théodore K. On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 457-475. http://geodesic.mathdoc.fr/item/CMUC_1999__40_3_a5/