Well-posedness in L∞(ℝn) (n ≥ 3) of the Cauchy problem is studied for a class of linear parabolic equations with variable density. In view of degeneracy at infinity, some conditions at infinity are possibly needed to make the problem well-posed. Existence and uniqueness results are proved for bounded solutions that satisfy either Dirichlet or Neumann conditions at infinity.
|Number of pages||13|
|Journal||St. Petersburg Mathematical Journal|
|State||Published - 2008|
- Bounded solutions
- Linear parabolic equations with variable density
- Parabolic Cauchy problem