The Cauchy Problem for the p-Laplacian Equation with a Nonlinear source

LEI Pei-dong

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The Cauchy Problem for the p-Laplacian Equation with a Nonlinear source

机译：具有非线性源的p-Laplacian方程的Cauchy问题。

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摘要

In this paper we study the existence and uniqueness of positive solutions for the p-Laplacian equation with nonlinear source аu/аt = div(│Du│~p-2Du) + u~-q, P > 2, 0 < q < ∞ in the class of functions with some prescribed growth rate as │x│→ ∞. We also give a description of the large time behaviour and show that it is determined by the competition between the diffusion and the source.

机译：在本文中，我们研究了带有非线性源аu/аt= div（│Du│〜p-2Du）+ u〜-q，P> 2，0

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来源
《Northeastern mathematical journal》 |2001年第1期|p.91-102|共12页
作者
LEI Pei-dong;
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正文语种 eng
中图分类数学;
关键词
p-Laplacian equation; existence; uniqueness;

机译：p-Laplacian方程;存在;独特性;

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专利

1. On the Cauchy Problem of Evolution P-Laplacian Equations with Strongly Non-linear sources When 1 <2 [J] . jun Ning Zhao, Pei Dong Lei Acta Mathematica Sinica . 2001,第3期

机译：1 <2时具有强非线性源的演化P-Laplacian方程的柯西问题
2. On the Cauchy problem for the evolution p-Laplacian equations with gradient term and source and measures as initial dataI [J] . Haifeng Shang, Fengquan Li Nonlinear Analysis: An International Multidisciplinary Journal . 2010,第7a8期

机译：以梯度项和源为度量的演化p-Laplacian方程的柯西问题和度量为初始数据I
3. On the Cauchy problem for the evolution p-Laplacian equations with gradient term and source [J] . Songzhe Lian, Hongjun Yuan, Chunling Cao, Journal of Differential Equations . 2007,第2期

机译：具有梯度项和源的演化p-Laplacian方程的柯西问题
4. A Nonlinear Evolution System of Partial Differential Equations With p-Laplacian and Negative Nonlineariy [C] . Nelson N. de O. Castro, Jorge Ferreira WSEAS MATH, TELE-INFO, SIP, CSECS International Conferneces . 2007

机译：具有P-Laplacian和负非线性的部分微分方程的非线性演化系统
5. Damped Wave Equations of the p-Laplacian Type with Supercritical Sources [D] . Kass, Nicholas J. 2018

机译：具有超临界源的p-Laplacian型阻尼波方程
6. Colloquium PaperNonlinear partial differential equations and applications: On the global Cauchy problem for the nonlinear Schrödinger equation [O] . Jean Bourgain 2007

机译：非线性偏微分方程及其应用：关于非线性的整体柯西问题薛定er方程
7. On the Cauchy Problem and Initial Traces for the Evolution p-Laplacian Equations with Strongly Nonlinear Sources [O] . Zhao J.N. 1995

机译：具有强非线性源的演化p-Laplacian方程的柯西问题和初始迹线

The Cauchy Problem for the p-Laplacian Equation with a Nonlinear source

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