On critical exponents for semilinear heat equations with nonlinear boundary conditions |
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Authors: | Lin Zhigui Xie Chunhong Wang Mingxin |
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Institution: | (1) Department of Mathematics, Teachers’ College, Yangzhou University, 225002 Yangzhou;(2) Department of Mathematics, Nanjing University, 210093 Nanjing;(3) Department of Mathematics and Mechanics, Southeast University, 210018 Nanjing |
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Abstract: | This paper deals with the blow-up properties of solutions to semilinear heat equation
with the nonlinear boundary condition
. It has been proved that if max(p,q)≤1,every nonnegative solution is global. When min(p, q)>1 by letting α=1/p−1 and β=1/2(q−1) it follows that if max (α,β)≤N/2,all nontrivial non-negative solutions are nonglobal, whereas if max(α,β)< N/2,there exist
both global and non-global solutions. Moreover, the exact blow-up rates are established.
The third author’s work was supported by the National Natural Science Foundation of China. |
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Keywords: | Semilinear heat equations nonlinear boundary conditions critial exponent blow-up rate |
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