一类多维反应扩散系统的先验估计

Primary estimates of approximate solutions for multidimensional reaction diffusion system

研究从生物物理学中提出的一类反应扩散系统的初边值问题,在关于非线性项的单调性和增长阶假设下,利用积分估计和重要不等式,得到了关于近似解的一系列先验估计。这些估计一方面说明了问题的解在非线性项的特殊情形下满足在不同的函数空间的有界性;另一方面,这些范数的有界性为证明解的存在性提供了可能。

Study the initial boundary value problem for the system of multidimensional reaction - diffusion equations, under some monotone and growth conditions by integral estimates skill and some important inequalities, obtain a series of integral estimates for approximate solutions. On the one hand, these estimates indicate the boundness of solutions to the problem in different functional spaces when the nonlinear terms satisfy some special conditions. On the other hand, the boundness of these norms provides the possibility of proving the existence of solutions to the problem.