Some results on reaction diffusion equations with initial time difference (Q2754456)

In the qualitative study of initial value problems as well as initial-boundary value problems, we have been partial to the independent variable in the sense that we only perturb the dependent variable or the space variable and keep the initial time unchanged. However, it is important to vary the initial time as well because it is impossible not to make errors in the starting time. For example, the solutions of the perturbed and unperturbed system may start at different initial time. Also, there are several ways of comparing two solutions which differ in time. To each choice of measuring the difference, we will end up with different results. Recently, some results are developed for first-order ordinary differential equations with initial time difference. In this paper, the author develops a comparison theorem, existence results by the method of upper and lower solutions and the monotone iterative technique respectively for reaction-diffusion equations with the initial time difference and Dirichlet boundary condition.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00018].