CAJ | 학술논문

该文是关于一类具有内吸收和耦合局部化源的抛物组解的渐近分析的研究.作者证明了解在区域内处处blow-up的结论,得到不同非线性指标占优情形下三种可能的blow-up速率,并借助于所引入的特征代数方程组给出这三种速率的简洁表示.特别地,作者对弱吸收情形,给出解的一致blow-up profile;对于两种非平衡吸收情形,得到与吸收项指标有关的blow-up速率,这与单个方程情形(其速率均与吸收项指标无关)的已有结果截然不同.以上结果的证明主要依据scaling方法,以及对于模型非线性指标的完全分类.
해문시관우일류구유내흡수화우합국부화원적포물조해적점근분석적연구.작자증명료해재구역내처처blow-up적결론,득도불동비선성지표점우정형하삼충가능적blow-up속솔,병차조우소인입적특정대수방정조급출저삼충속솔적간길표시.특별지,작자대약흡수정형,급출해적일치blow-up profile;대우량충비평형흡수정형,득도여흡수항지표유관적blow-up속솔,저여단개방정정형(기속솔균여흡수항지표무관)적이유결과절연불동.이상결과적증명주요의거scaling방법,이급대우모형비선성지표적완전분류.
This paper deals with asymptotic analysis to a parabolic model with absorptions and coupled localized sources,for which it is shown that any blow-up occurs everywhere in the domain with one of three possible simultaneous blow-up rates under different dominations of nonlinearities. All the three blow-up rates are simply represented in a characteristic algebraic system introduced for the problem. In particular,uniform blow-up profiles are established for the case of weak absorptions. While for the two cases of unbalanced absorptions,we estab-lish uniform blow-up rates (instead of blow-up profiles) which are absorption-related. This is substantially different from scalar parabolic problems with absorptions in current literatures,where all the blow-up rates are known as absorption-independent. The results of the paper mainly rely on the scaling method with a complete classification for the nonlinear parameters in the model.