Uniqueness of renormalized solutions for a class of parabolic equations with unbounded nonlinearities

Abstract

We prove uniqueness and a comparison principle of renormalized solutions for a class of doubly nonlinear parabolic equations ∂b(x,u)/∂t − div(A(t, x)Du + Φ(u)) = f, where the right side belongs to L1((0, T) × Ω) and where b(x, u) is unbounded function of u and where A(t, x) is a bounded symmetric and coercive matrix, and Φ is continuous function but without any growth assumption on u.

Keywords

• nonlinear parabolic equations
• uniqueness
• renormalized solutions