Blow-up for Discrete Reaction-Diffusion Equations on Networks
- 발행기관 서강대학교 일반대학원
- 지도교수 정순영
- 발행년도 2014
- 학위수여년월 2014. 2
- 학위명 석사
- 학과 및 전공 도움말 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/sogang/000000053359
- 본문언어 영어
- 저작권 서강대학교 논문은 저작권 보호를 받습니다.
초록/요약 도움말
We discuss the conditions under which blow-up occurs for the solutions of reactiondiffusion equations on networks as follows: ??? ?? ut ? !u = uq in S × (0,∞), u = 0 on @S × (0,∞), u(·, 0) = u0 on S. Here S is a simple and connected graph with a weight !, the operator ! is the discrete Laplacian and q > 0. The initial data u0 are non-negative on S and non-trivial on S. The main theorem states that (i) if q > 1 and yq?1 0 > K · |S|q?1, then the solution blows up, (ii) if 0 < q ≤ 1, then the solution is global, where y0 = X x∈S u0(x) and K = max x∈S X y∈@S !(x, y). In addition, when the solution blows up, we give estimates for the blow-up time and also provide the blow-up rate. Finally, we show some numerical illustrations which describe the main results. Key words : Reaction-diffusion; Discrete Laplacian; Comparison Principle; Blow-up
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