On correctness of the Fourier problem for a nonstationary filtering system without conditions at the infinity. (Ukrainian) Zbl 0929.35021
Summary: The Fourier problem (a problem without initial conditions) for a nonstationary filtering system is investigated. The existence and uniqueness conditions of a generalized solution are obtained without assumptions on the behaviour and the growth of the initial data at infinity. Continuous dependence of solutions on the right terms of the equations is established.
MSC:
| 35D05 | Existence of generalized solutions of PDE (MSC2000) |
| 35K50 | Systems of parabolic equations, boundary value problems (MSC2000) |
| 35B45 | A priori estimates in context of PDEs |
| 35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
