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
\[
\begin{cases} u_t-\Delta_pu=\mu & \text{in}\;(0,T)\times\Omega,\\ u(0,x)=u_0 & \text{in}\;\Omega,\\ u(t,x)=0 & \text{on}\;(0,T)\times\partial\Omega, \end{cases}
\]
where \(\Omega\subset\mathbb R^n\), \(n\geq2,\) is a bounded and open set and \(\mu\in M(Q)\) is a measure with bounded variation over \(Q=(0,T)\times\Omega.\)
Reviewer: Dian K. Palagachev (Bari)
MSC:
| 35K55 | Nonlinear parabolic equations |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35D05 | Existence of generalized solutions of PDE (MSC2000) |
| 35D10 | Regularity of generalized solutions of PDE (MSC2000) |
| 35R05 | PDEs with low regular coefficients and/or low regular data |
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