學術活動
Stability of Traveling Wave fronts For Time-Delayed Reaction-Diffusion Equations
2009-06-30
來源：科技處 點擊次數：主講人： Professor Ming Mei (Champlain College St.-Lambert & McGill University, Canada)
时 间：7月3日（星期五）下昼15：00-16：00
地 点： 數學科學學院412 课堂
主 办： 數學科學學院
摘 要：This is a series of study on the stability of traveling wavefronts for a class of time-delayed reactions--diffusion equations with local /nonlocal nonlinearity for the birth rate. When the initial perturbation around the traveling wave decays exponentially as x to negative infinity (but the initial perturbation can be arbitrarily large in other locations), we prove the asymptotic stability of all traveling waves for the reaction--diffusion equation, including even the critical wave. This essentially improves the our previous stability results for fast wave stability with a small initial perturbation. The approach we use here is the weighted energy method with the comparison principle together, but the weight function is more tricky to construct due to the property of the critical wavefront, and the difficulty arising from the nonlocal nonlinearity is also overcome. Finally, by using the Crank-Nicolson scheme, we present some numerical results which confirm our theoretical study.
