一类Volterra反应扩散方程

ON A CERTAIN CLASS OF VOLTERRA REACTION DIFUSION EQUATIONS

我们在本文考虑带Robin边界条件的半线性Volterra生物群体反应扩散方程u_t=Lu-bu^2-uf*u其中L是具有光滑系数a_(ti),a_i的二阶线性一致椭圆算子。此外,a,b是某些正常数,f*u是由ds定义的卷积。我们确定了非负全局有界解的存在性和唯一性,并且证明了当t→∞时解的渐近性质。我们的主要工具是Banach不动点原理和比较方法。

In this paper we consider semilinear Volterra population reaction diffusion equation u_t=Lu-bu^2-uf*u with Robin boundary condition,where, Lu is a second order linear uniformly elliptic operator Lu=au with Smooth coefficients α_(i1), α_i, in addi-tion, a, b are some positive constants, f*u denote convolution definedExistence and uniqueness of globalnonnegative bounded solution are established and the asymptotic beha-viour of the solution as t→∞ is proved. Our main tools are the fixedpoint principle of Banach and the comparison method.