Event
01_1
| 제출번호(No.) | 0092 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Analysis (AN) |
| 영문제목 (Title(Eng.)) |
A complete characterization of parameters of the discrete p-Laplacian nonlinear parabolic equations with q-nonlocal reaction with respect to the blow-up property |
| 저자(Author(s)) |
Jaeho Hwang1, Soon-Yeong Chung1 Sogang University1 |
| 초록본문(Abstract) | In this talk, we consider discrete $p$-Laplacian nonlinear parabolic equations with $q$-nonlocal reaction under Dirichlet boundary condition as follows: \begin{equation*} \begin{cases} u_{t}\left(x,t\right) = \Delta_{p,\omega} u\left(x,t\right) +\lambda \sum_{y \in S} \left\vert u\left(x,t\right) \right\vert^{q-1} u\left(x,t\right), &\left(x,t\right) \in S \times \left(0,\infty\right), \\ u\left(x,t\right) = 0, &\left(x,t\right) \in \partial S \times \left(0,\infty\right), \\ u\left(x,0\right) = u_{0} \geq 0, &x \in \overline{S}. \end{cases} \end{equation*} Here, $S$ is a network with boundary $\partial S$. The parameters $p>1$, $q>0$ are completely characterized to see when the solution blows up, vanishes, or exists globally. Indeed, the blow-up rates when blow-up does occur are derived. Also, we give some numerical experiments which explain the main results. |
| 분류기호 (MSC number(s)) |
39A12, 39A13, 39A70, 35K57 |
| 키워드(Keyword(s)) | discrete p-Laplacian, semilinear parabolic equation, nonlocal reaction, blow-up |
| 강연 형태 (Language of Session (Talk)) |
Korean |