For a given bounded domain <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\Omega \subset \mathbb R^3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Ω</mi> <mo>⊂</mo> <msup> <mi mathvariant="double-struck">R</mi> <mn>3</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>, with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$C^2$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> boundary, and a given instant of time <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$T>0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>T</mi> <mo>></mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, we prove the existence of a global weak solution on (0, T), which satisfies a maximum principle, to a parabolic p-Laplacian system with convective term without divergence constraint for any <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$p\in (1,2)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and the initial datum in <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$L^\infty (\Omega )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mi>∞</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Moreover, we study the finite-time extinction property for suitable initial data.

Existence of Global Weak Solutions to a Parabolic p-Laplacian Problem with Convective Term

期刊论文
出版模式：

开放获取
发表日期：

2026年7月22日

查看全文

Angelica Pia Di Feola,
Michael Růžička

摘要

For a given bounded domain $\Omega \subset \mathbb R^3$ $Ω \subset R^{3}$ , with $C^2$ $C^{2}$ boundary, and a given instant of time $T>0$ $T > 0$ , we prove the existence of a global weak solution on (0, T), which satisfies a maximum principle, to a parabolic p-Laplacian system with convective term without divergence constraint for any $p\in (1,2)$ $p \in (1, 2)$ and the initial datum in $L^\infty (\Omega )$ $L^{\infty} (Ω)$ . Moreover, we study the finite-time extinction property for suitable initial data.