Comparison results for unbounded solutions for a parabolic Cauchy-Dirichlet problem with superlinear gradient growth
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2017
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| _version_ | 1866929683529990144 |
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| author | Leonori, Tommaso Magliocca, Martina |
| author_facet | Leonori, Tommaso Magliocca, Martina |
| contents | In this paper we deal with uniqueness of solutions to the following problem \[ \begin{cases} \begin{split} & u_t-Δ_p u=H(t,x,\nabla u) &\quad \text{in}\quad Q_T,\\ & u (t,x) =0 &\quad \text{on}\quad(0,T)\times \partial Ω,\\ & u(0,x)=u_0(x) &\quad \displaystyle\text{in }\quad Ω\end{split} \end{cases} \] where $Q_T=(0,T)\times Ω$ is the parabolic cylinder, $Ω$ is an open subset of $\mathbb{R}^N$, $N\ge2$, $1<p<N$, and the right hand side $\displaystyle H(t,x,ξ):(0,T)\timesΩ\times \mathbb{R}^N\to \mathbb{R}$ exhibits a superlinear growth with respect to the gradient term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1711_06634 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Comparison results for unbounded solutions for a parabolic Cauchy-Dirichlet problem with superlinear gradient growth Leonori, Tommaso Magliocca, Martina Analysis of PDEs In this paper we deal with uniqueness of solutions to the following problem \[ \begin{cases} \begin{split} & u_t-Δ_p u=H(t,x,\nabla u) &\quad \text{in}\quad Q_T,\\ & u (t,x) =0 &\quad \text{on}\quad(0,T)\times \partial Ω,\\ & u(0,x)=u_0(x) &\quad \displaystyle\text{in }\quad Ω\end{split} \end{cases} \] where $Q_T=(0,T)\times Ω$ is the parabolic cylinder, $Ω$ is an open subset of $\mathbb{R}^N$, $N\ge2$, $1<p<N$, and the right hand side $\displaystyle H(t,x,ξ):(0,T)\timesΩ\times \mathbb{R}^N\to \mathbb{R}$ exhibits a superlinear growth with respect to the gradient term. |
| title | Comparison results for unbounded solutions for a parabolic Cauchy-Dirichlet problem with superlinear gradient growth |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1711.06634 |