We investigate the well-posedness of the Cauchy problem for a class of nonlinear parabolic equations with variable density. Sufficient conditions for uniqueness or nonuniqueness in L∞(IRN × (0, T)) (N ≥ 3) are established in dependence of the behavior of the density at infinity. We deal with conditions at infinity of Dirichlet type, and possibly inhomogeneous.
On the Cauchy problem for nonlinear parabolic equations with variable density / F. Punzo. - In: JOURNAL OF EVOLUTION EQUATIONS. - ISSN 1424-3199. - 9:3(2009), pp. 429-447. [10.1007/s00028-009-0018-6]
On the Cauchy problem for nonlinear parabolic equations with variable density
F. Punzo
2009
Abstract
We investigate the well-posedness of the Cauchy problem for a class of nonlinear parabolic equations with variable density. Sufficient conditions for uniqueness or nonuniqueness in L∞(IRN × (0, T)) (N ≥ 3) are established in dependence of the behavior of the density at infinity. We deal with conditions at infinity of Dirichlet type, and possibly inhomogeneous.
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