Abstract
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.
Original language | English |
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Pages (from-to) | 239-251 |
Number of pages | 13 |
Journal | St. Petersburg Mathematical Journal |
Volume | 19 |
Issue number | 2 |
DOIs | |
State | Published - 2008 |
Keywords
- Bounded solutions
- Linear parabolic equations with variable density
- Parabolic Cauchy problem