Existence and well-posed results for nonclassical diffusion systems with nonlocal diffusion

Abstract

Our goal in this paper is to present well-posed results for nonclassical diffusion systems which have applications in population dynamics. First, we establish the existence and uniqueness of a mild solution to the initial value problem. The asymptotic behavior of the mild solution is also considered when the parameter tends to zero. Second, we obtain a local well-posedness result for nonclassical diffusion systems with a nonlocal time condition. The main idea to obtain the above theoretical results is to use Banach’s theorem and some techniques in Fourier series analysis. Some numerical tests are also presented.