The well-posedness of the Fourier problem for quasilinear parabolic equations of arbitrary order in unisotropic spaces. (English) Zbl 0929.35022
Summary: The existence and uniqueness of a generalized solution of the Fourier problem is proved for a class of quasilinear parabolic equations of higher order in unisotropic Sobolev spaces. There are no restrictions on the behaviour of the solution and increasing of the entrance data at \( t\to-\infty\). Moreover, the continuous dependence of the generalized solution of this problem on the right side of the equation has been obtained.
MSC:
| 35D05 | Existence of generalized solutions of PDE (MSC2000) |
| 35K25 | Higher-order parabolic equations |
| 35K35 | Initial-boundary value problems for higher-order parabolic equations |
| 35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
| 35K55 | Nonlinear parabolic equations |
