Critical exponents for nonlinear diffusion equations with nonlinear boundary sources |
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| Authors: | Peter YH Pang Jingxue Yin |
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| Institution: | a Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543
b Department of Mathematics, Jilin University, Changchun 130012, PR China |
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| Abstract: | This paper is concerned with the large time behavior of solutions to two types of nonlinear diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball. We are interested in the critical global exponent q0 and the critical Fujita exponent qc for the problems considered, and show that q0=qc for the multi-dimensional porous medium equation and non-Newtonian filtration equation with nonlinear boundary sources. This is quite different from the known results that q0<qc for the one-dimensional case. |
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| Keywords: | Critical global exponent Critical Fujita exponent Nonlinear diffusion equation |
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