We prove the well-posedness of Fourier problems for anisotropic elliptic-parabolic equations with variable exponents of nonlinearity without any restrictions at infinity. We obtain estimates of the weak solutions and conditions for the existence of periodic and almost periodic solutions. In addition, some properties of the weak solutions of the Fourier problem are considered.
Submitted April 17, 2014. Published August 11, 2014.
Math Subject Classifications: 35K10, 35K55, 35K92.
Key Words: Fourier problem; problem without initial conditions; degenerate implicit equations; elliptic-parabolic equation; periodic solution; almost periodic solution; nonlinear evolution equation.
Show me the PDF file (272 KB), TEX file, and other files for this article.
| Mykola Bokalo |
Department of Differential Equations
Ivan Franko National University of Lviv
Return to the EJDE web page