Very singular solution and short time asymptotic behaviors of nonnegative singular solutions for heat equation with nonlinear convection

Guofu Lu

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Very singular solution and short time asymptotic behaviors of nonnegative singular solutions for heat equation with nonlinear convection

机译：具有非线性对流的热方程中非负奇异解的非常奇异的解决方案和短时渐近性行为

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Abstract

In this paper we study the following Cauchy problem:ut=uxx+(un)x,(x,t)∈R×(0,∞),u(x,0)=0,x≠0,where parametern≥

机译：<！[cdata [ Abstract

在本文中，我们研究了以下Cauchy问题： U T = U X X + （ U N ） x ，（ x ， < MML：MI> T ） ∈ R × （ 0 ， ∞ ）， u （ x ， 0 ） = 0 ， X ≠ 0 ，其中参数 n ≥

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来源
《Journal of Differential Equations》 |2017年第12期|共47页
作者
Guofu Lu;
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作者单位

Institute of Applied Mathematics Putian University;

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原文格式 PDF
正文语种 eng
中图分类微分方程、积分方程;
关键词
Nonlinear convection; Source-type solution; Very singular solution; Critical exponent; Asymptotic behaviors; Entropy inequality;

机译：非线性对流;源型解决方案;非常奇异的解决方案;批判性指数;渐近行为;熵不平等;

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专利

1. Very singular solution and short time asymptotic behaviors of nonnegative singular solutions for heat equation with nonlinear convection [J] . Guofu Lu Journal of Differential Equations . 2017,第12期

机译：具有非线性对流的热方程中非负奇异解的非常奇异的解决方案和短时渐近性行为
2. On the asymptotic behavior of solutions of differential equations with a singular nonlinearity [J] . Astashova I. V. Differential equations: A translation of differensial'nye uraveniya . 2014,第11期

机译：具有奇异非线性的微分方程解的渐近性质
3. ASYMPTOTIC BEHAVIOR OF BLOWUP SOLUTIONS FOR ELLIPTIC EQUATIONS WITH EXPONENTIAL NONLINEARITY AND SINGULAR DATA [J] . Zhang L Communications in contemporary mathematics . 2009,第3期

机译：具有指数非线性和奇异数据的椭圆型方程爆破解的渐近性质。
4. Problems involved in elimination of both the singularity in the solution of nonlinear equation of motion on the rotation axis and the unbalance caused by convective heat transfer [C] . Yu. V. Vandakurov, E. M. Sklyarova International Astronomical Union . 2004

机译：消除旋转轴上非线性运动溶液中的奇异性的问题以及对流传热引起的不平衡
5. Uniqueness and singularities of weak solutions to some nonlinear wave equations. [D] . Zhang, Qingtian. 2016

机译：某些非线性波动方程弱解的唯一性和奇异性。
6. Multiplicity and asymptotic behavior of solutions for Kirchhoff type equations involving the Hardy–Sobolev exponent and singular nonlinearity [O] . Liejun Shen -1

机译：具有Hardy-Sobolev指数和奇异非线性的Kirchhoff型方程解的多重性和渐近性
7. Multiplicity and asymptotic behavior of solutions for Kirchhoff type equations involving the Hardy–Sobolev exponent and singular nonlinearity [O] . Liejun Shen 2018

机译：Kirchhoff型方程解决方案的多重性和渐近行为涉及Hardy-Sobolev指数和奇异非线性

Very singular solution and short time asymptotic behaviors of nonnegative singular solutions for heat equation with nonlinear convection

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