In this paper we deal with uniqueness of solutions to the following problem $\begincases \beginsplit & u_t-\Delta_p u=H(t,x,\nabla u) &\quad \textin\quad Q_T,\\ & u (t,x) =0 &\quad \texton\quad(0,T)\times \partial \Omega,\\ & u(0,x)=u_0(x) &\quad \displaystyle\textin \quad \Omega \endsplit \endcases$ where $Q_T=(0,T)\times \Omega$ is the parabolic cylinder, $\Omega$ is an open subset of $\mathbbR^N$, $N\ge2$, $1<p<N$, and the right hand side $\displaystyle H(t,x,\xi):(0,T)\times\Omega \times \mathbbR^N\to \mathbbR$ exhibits a superlinear growth with respect to the gradient term.

Comparison results for unbounded solutions for a parabolic Cauchy-Dirichlet problem with superlinear gradient growth / Leonori, Tommaso; Martina, Magliocca; Magliocca, Martina. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - (2019).

### Comparison results for unbounded solutions for a parabolic Cauchy-Dirichlet problem with superlinear gradient growth

#### Abstract

In this paper we deal with uniqueness of solutions to the following problem $\begincases \beginsplit & u_t-\Delta_p u=H(t,x,\nabla u) &\quad \textin\quad Q_T,\\ & u (t,x) =0 &\quad \texton\quad(0,T)\times \partial \Omega,\\ & u(0,x)=u_0(x) &\quad \displaystyle\textin \quad \Omega \endsplit \endcases$ where $Q_T=(0,T)\times \Omega$ is the parabolic cylinder, $\Omega$ is an open subset of $\mathbbR^N$, $N\ge2$, \$1
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Mathematics - Analysis of PDEs; Mathematics - Analysis of PDEs
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Comparison results for unbounded solutions for a parabolic Cauchy-Dirichlet problem with superlinear gradient growth / Leonori, Tommaso; Martina, Magliocca; Magliocca, Martina. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - (2019).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1212361