Existence of a Sign-Changing Weak Solution to Doubly Nonlinear Parabolic Equations
Existence of a Sign-Changing Weak Solution to Doubly Nonlinear Parabolic Equations
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双非线性抛物型方程变号弱解的存在性
DOI：
10.1007/s12220-022-01087-8
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Kenta Nakamura
中科院分区：
文献类型：
--
作者：
Masashi misawa;Kenta Nakamura
In this paper, assuming the initial-boundary datum belonging to suitable Sobolev and Lebesgue spaces, we prove the global existence result for a (possibly sign changing) weak solution to the Cauchy–Dirichlet problem for doubly nonlinear parabolic equations of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \partial _t\left( |u|^{q-1}u\right) -\Delta _p u=0\quad \text {in}\,\,\,\Omega _\infty , \end{aligned}$$\end{document}whereand. This is a fair improvement of the preceding result by authors (Nonlinear Anal 175C :157–172, 2018). The key tools we employ are energy estimates for approximate equations of Rothe type and the integral strong convergence of gradients of approximate solutions.
In this paper, assuming the initial-boundary datum belonging to suitable Sobolev and Lebesgue spaces, we prove the global existence result for a (possibly sign changing) weak solution to the Cauchy–Dirichlet problem for doubly nonlinear parabolic equations of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \partial _t\left( |u|^{q-1}u\right) -\Delta _p u=0\quad \text {in}\,\,\,\Omega _\infty , \end{aligned}$$\end{document}whereand. This is a fair improvement of the preceding result by authors (Nonlinear Anal 175C :157–172, 2018). The key tools we employ are energy estimates for approximate equations of Rothe type and the integral strong convergence of gradients of approximate solutions.
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DOI：
10.1016/j.na.2018.05.016
发表时间：
2018-10
期刊：
Nonlinear Analysis
影响因子：
--
作者：
Kenta Nakamura;M. Misawa
通讯作者：
Kenta Nakamura;M. Misawa
双非线性抛物型方程的本征标度法及其应用
影响因子：
1.7
作者：
M. Misawa;Kenta Nakamura
通讯作者：
Kenta Nakamura
上层 Wärmeleitungsgleichung mit nichtkonstanten Koeffizienten im räumlichen Falle
影响因子：
1.4
作者：
Erich H. Rothe
通讯作者：
Erich H. Rothe
影响因子：
2.4
作者：
Tuomo Kuusi;M. Misawa;Kenta Nakamura
通讯作者：
Tuomo Kuusi;M. Misawa;Kenta Nakamura
影响因子：
2.5
作者：
Boegelein, Verena;Duzaar, Frank;Scheven, Christoph
通讯作者：
Scheven, Christoph