On the notion of renormalized solution to nonlinear parabolic equations with general measure data

2015/06/30 by Francesco Petitta, Alessio Porretta · 1 citation
Mathematics · #math.AP

paper · pdf

published as J. of Elliptic and Parabolic Equations, 1, (2015), 201-214

arxiv created 2017/02/14 · arxiv updated 2017/02/15

Abstract

Here we introduce a new notion of renormalized solution to nonlinear parabolic problems with general measure data whose model is \begincases u_t-Δ_p u =μ in (0,T)×Ω, u=u₀ on \0\ × Ω, u=0 on (0,T)×∂Ω, \endcases for any, possibly singular, nonnegative bounded measure μ. We prove existence of such a solutions and we discuss their main properties.

Cited by

• Nonlinear parabolic equations with soft measure data

Related

• Diffuse measures and nonlinear parabolic equations
• Nonlinear parabolic equations with soft measure data
• Parabolic equations with exponential nonlinearity and measure data
• Potential estimates and quasilinear parabolic equations with measure data
• Existence and uniqueness for renormalized solutions to a general noncoercive nonlinear parabolic equation