ИСТИНА

The paper deals with three-dimensional nonlinear reaction-diffusion equations with delay. We formulate and prove theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. A number of test problems which can be suitable for examining well-posedness and estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented.