Geodesic
Blow-up of sign-changing solutions to quasilinear parabolic equations
Informatics and Automation, Function theory and differential equations, Tome 269 (2010), pp. 215-224

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We study the blow-up of sign-changing solutions to the Cauchy problem for quasilinear parabolic equations of arbitrary order. Our approach is based on H. Levine's remarkable idea of constructing a concavity inequality for a negative power of a standard positive definite functional. Combining this with the nonlinear capacity method, which is based on the choice of optimal test functions, we find conditions for the blow-up of solutions to the problems under consideration. 
@article{TRSPY_2010_269_a17,
     author = {S. I. Pohozaev},
     title = {Blow-up of sign-changing solutions to quasilinear parabolic equations},
     journal = {Informatics and Automation},
     pages = {215--224},
     publisher = {mathdoc},
     volume = {269},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2010_269_a17/}
}
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S. I. Pohozaev. Blow-up of sign-changing solutions to quasilinear parabolic equations. Informatics and Automation, Function theory and differential equations, Tome 269 (2010), pp. 215-224. http://geodesic.mathdoc.fr/item/TRSPY_2010_269_a17/