无界域上部分耗散系统解的全局存在性和唯一性(英文)

The existence and uniqueness of the solutions for partly dissipative reaction diffusion systems in R^n

为了包含常数解以及行波解等特殊形式的解,用加权空间作为相空间。考虑了带有任意阶多项式增长指数非线性项的部分耗散系统,证明了系统所对应的解在L_〈r〉~2(R^n)×L_〈r〉~2(R^n)(r＞n/2)中的全局存在性以及唯一性．

This paper proves the existence and uniqueness of the solutions for the partly dissipative reaction diffusion system with some weak derivatives and with a polynomial growth nonlinearity of arbitrary order in inhomogeneous term. The solutions are obtained in the weighted space L^2（γ）（R^n） × L^2（γ）（R^n）, which allows functions to grow at infinity.