Existence of peaking solutions for semilinear heat equations with blow-up profile above the singular steady state

Naito Yuki; Senba Takasi

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Existence of peaking solutions for semilinear heat equations with blow-up profile above the singular steady state

机译：半线性热方程峰值溶液的存在性爆破轮廓上方奇异稳态

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摘要

We consider positive solutions of the semilinear heat equation with supercritical power nonlinearity, and construct peaking solutions by connecting a backward self-similar solution with a forward self-similar solution. In particular, we show the existence of incomplete blow-up solutions with blow-up profile above the singular steady state. We also show the existence of a minimal continuation and obtain some properties of non-minimal continuations. (C) 2018 Elsevier Ltd. All rights reserved.

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来源
《Nonlinear Analysis: An International Multidisciplinary Journal》 |2019年第2019期|共29页
作者
Naito Yuki; Senba Takasi;
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作者单位

Ehime Univ Grad Sch Sci &

Engn Dept Math Matsuyama Ehime 7908577 Japan;

Fukuoka Univ Fac Sci Fukuoka Fukuoka 8140180 Japan;

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原文格式 PDF
正文语种 eng
中图分类数学分析;
关键词
Semilinear heat equation; Incomplete blow-up; Self-similar solution; Peaking solution;

机译：半线性热方程;不完全爆炸;自相似的解决方案;峰值溶液;

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专利

1. Existence of peaking solutions for semilinear heat equations with blow-up profile above the singular steady state [J] . Naito Yuki, Senba Takasi Nonlinear Analysis: An International Multidisciplinary Journal . 2019,第期

机译：半线性热方程峰值溶液的存在性爆破轮廓上方奇异稳态
2. Existence, non-existence and asymptotic behavior of blow-up entire solutions of semilinear elliptic equations [J] . Goncalves JV, Roncalli A Journal of Mathematical Analysis and Applications . 2006,第2期

机译：半线性椭圆型方程爆破整体解的存在性，不存在性和渐近性
3. GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS FOR INFINITELY DEGENERATE SEMILINEAR PSEUDO-PARABOLIC EQUATIONS WITH LOGARITHMIC NONLINEARITY [J] . Chen Hua, Xu Huiyang Discrete and continuous dynamical systems . 2019,第2期

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4. Existence and blow-up of solutions for a degenerate semilinear parabolic equation [C] . Yanping Ran, Congming Peng International Conference on Chemical Engineering and Advanced Materials . 2013

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5. Global Existence of Solutions to Semilinear Klein-Gordon Equations [D] . Pikula, Nina. 2019

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6. Existence of anti-periodic (differentiable) mild solutions to semilinear differential equations with nondense domain [O] . Jinghuai Liu, Litao Zhang -1

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7. Existence, non-existence and asymptotic behavior of blow-up entire solutions of semilinear elliptic equations [O] . Goncalves J.V., Roncalli Angelo 2006

机译：半线性椭圆型方程爆破整体解的存在性，不存在性和渐近性
8. Structure of the Set of Steady-State Solutions and Asymptotic Behaviour of Semilinear Heat Equations [R] . Lions, P. L. 1981

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Existence of peaking solutions for semilinear heat equations with blow-up profile above the singular steady state

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