Critical exponent of blowup for semilinear heat equation on a product domain
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概要
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We show that for many regions of product type $D=D_1 \times D_2$ the critical exponent of blowup for the Dirichlet mixed problem of the semilinear heat equation ${\partial}_t u= \Delta u +u^p$ is determined from those of the factors by the formula $1/(p^* (D) -1)=1/(p^* (D_1)-1)+1/(p^* (D_2)-1)$. As an application we obtain a formula for the first Dirichlet eigenvalue of the Laplace-Beltrami operator on spherical slice domains.
- Faculty of Science, The University of Tokyoの論文
Faculty of Science, The University of Tokyo | 論文
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