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Zbl 1150.35060
Petitta, Francesco
Renormalized solutions of nonlinear parabolic equations with general measure data.
(English)
[J] Ann. Mat. Pura Appl. (4) 187, No. 4, 563-604 (2008). ISSN 0373-3114; ISSN 1618-1891/e

The author proves the existence of a renormalized solution of the following initial-boundary value problem for the parabolic $p$-Laplacian $$\cases u_t-\Delta_pu=\mu & \text{in}\ (0,T)\times\Omega,\\ u(0,x)=u_0 & \text{in}\ \Omega,\\ u(t,x)=0 & \text{on}\ (0,T)\times\partial\Omega, \endcases$$ where $\Omega\subset\Bbb R^n$, $n\geq2,$ is a bounded and open set and $\mu\in M(Q)$ is a measure with bounded variation over $Q=(0,T)\times\Omega.$
[Dian K. Palagachev (Bari)]
MSC 2000:
*35K55 Nonlinear parabolic equations
35K20 Second order parabolic equations, boundary value problems
35D05 Existence of generalized solutions of PDE
35D10 Regularity of generalized solutions of PDE
35R05 PDE with discontinuous coefficients or data

Keywords: nonlinear parabolic equations; parabolic capacity; measure data

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