논문
[기관장]An application of FDM by Gibou to a numerical blow-up for nonlinear evolution equations on a domain Ω⊂ R N
- 저자Soon-Yeong Chung, Jea-Hyun Park
- 학술지Communications in Mathematical Sciences 17(4)
- 등재유형
- 게재일자(2019)
In this paper, using finite difference method introduced by Gibou et al., we show the blow-up phenomenon of solutions to nonlinear evolution equations with Dirichlet boundary condition on an N-dimensional smooth bounded domain.
We first present bounds of the discrete smallest eigenvalue and the corresponding eigenfunction to the discrete Dirichlet eigenvalue problem with the discrete Laplacian which is obtained by Gibou's method. We also show that exists a blow-up time of the numerical solution by finding upper and lower bounds of the blow-up time. Finally, using the above results, we prove that the theoretical solution has a blow-up time and we also give upper and lower bounds for the blow-up time of the theoretical solution.
In this paper, using finite difference method introduced by Gibou et al., we show the blow-up phenomenon of solutions to nonlinear evolution equations with Dirichlet boundary condition on an N-dimensional smooth bounded domain.
We first present bounds of the discrete smallest eigenvalue and the corresponding eigenfunction to the discrete Dirichlet eigenvalue problem with the discrete Laplacian which is obtained by Gibou's method. We also show that exists a blow-up time of the numerical solution by finding upper and lower bounds of the blow-up time. Finally, using the above results, we prove that the theoretical solution has a blow-up time and we also give upper and lower bounds for the blow-up time of the theoretical solution.
