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Renormalized solutions of nonlinear parabolic equations with general measure data. (English) Zbl 1150.35060

The author proves the existence of a renormalized solution of the following initial-boundary value problem for the parabolic p-Laplacian

u t -Δ p u=μin(0,T)×Ω,u(0,x)=u 0 inΩ,u(t,x)=0on(0,T)×Ω,

where Ω n , n2, is a bounded and open set and μM(Q) is a measure with bounded variation over Q=(0,T)×Ω·

MSC:
35K55Nonlinear parabolic equations
35K20Second order parabolic equations, initial boundary value problems
35D05Existence of generalized solutions of PDE (MSC2000)
35D10Regularity of generalized solutions of PDE (MSC2000)
35R05PDEs with discontinuous coefficients or data
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