CAJ | 학술논문

研究了具有对数奇性耦合的半线性抛物方程组的初边值问题,利用上、下解法和特征函数法,得到了当区域的直径小于某个常数时解是全局存在的,当区域的直径适当大时,解会在有限时刻发生猝灭,并给出了猝灭时刻的上、下界的估计.
연구료구유대수기성우합적반선성포물방정조적초변치문제,이용상、하해법화특정함수법,득도료당구역적직경소우모개상수시해시전국존재적,당구역적직경괄당대시,해회재유한시각발생졸멸,병급출료졸멸시각적상、하계적고계.
In this paper, a kind of initial-boundary-value problems for semilinear parabolic system with logarithmic singular coupling is studied. By the method of upper and lower solution and the method of eigenfunction, it is proved that the solutions of the problem are global for adequate small region such that the diameter of the region less than certain constant while the solutions quench in finite time for adequate large region. The upper and lower bound of quenching time is estimated.