带时间依赖扩散系数的分数阶非经典扩散方程的适定性

Well-posedness for Fractional Nonclassical Diffusion Equations with Time-dependent Diffusion Coefficients

本文讨论带有时间依赖扩散系数的分数阶非经典扩散方程的适定性问题,运用非经典的Faedo-Galerkin方法、插值不等式以及控制收敛原理,得到方程在分数阶Sobolev空间Η^(θ)(0<θ≤1)中整体弱解的存在性、唯一性及其对初值的连续依赖性,其中非线性项满足任意阶多项式增长条件.

This paper discusses the well-posedness problem of fractional nonclassical diffusion equations with time-dependent dissipation coefficients.Using the nonclassical Faedo-Galerkin method,the interpolation inequality and the control convergence principle,the existence,uniqueness and continuous dependence on initial values of the global weak solution in Η^(θ)(0<θ≤1)for the equations are obtained,where the nonlinearity f satisfies the polynomial growth of arbitrary order.