Abstract
We consider nonnegative solutions to the Cauchy problem for the quasilinear parabolic equations where , and has the following properties: - as in some cone and in the complement of , where for we define that has a compact support. We find a critical exponent such that if , then every nontrivial nonnegative solution is not global in time; whereas if then there exits a global solution. We also find a second critical exponent, which is another critical exponent on the growth order of the initial data such that - as in some cone and in the complement of .
Citation
Ryuichi SUZUKI. "Existence and nonexistence of global solutions of quasilinear parabolic equations." J. Math. Soc. Japan 54 (4) 747 - 792, October, 2002. https://doi.org/10.2969/jmsj/1191591992
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