On a Fourier problem for a coupled system of evolution equations with time delays. (English) Zbl 1023.35046
Summary: A problem without initial conditions for coupled systems of parabolic ordinary equations with time delay is investigated. Theorems on a priori estimate, uniqueness, and existence of a solution of such problem are proved. Continuous dependence of the solution on the data is established.
MSC:
35K50 | Systems of parabolic equations, boundary value problems (MSC2000) |
35R10 | Partial functional-differential equations |
35K57 | Reaction-diffusion equations |
35K35 | Initial-boundary value problems for higher-order parabolic equations |