Volume 17, Issue 4
Existence and Nonexistence of Global Solutions for Semilinear Heat Equation on Unbounded Domain

Yonggeng Gu & Wenjun Sun

J. Part. Diff. Eq., 17 (2004), pp. 351-368.

Published online: 2004-11

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  • Abstract

In this paper, we consider the existence and nonexistence of global solutions to the semilinear heat equation u_t - Δu = u^p with Neumann boundary value \frac{∂u}{∂ν} = 0 on some unbounded domains, where p > 1, ν is the outward normal vector on boundary ∂Ω. We prove that there exists a critical exponent p_c = p_c(Ω) > 1 such that if p ∈ (1, p_c], for nonnegative and nontrivial initial data, all positive solutions blow up in finite time; if p > p_c, for suitably small nonnegative initial data, there exists a global positive solution.

  • Keywords

Semilinear heat equation global existence critical exponent of Fu-jita' s type

  • AMS Subject Headings

35K20 35K55

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COPYRIGHT: © Global Science Press

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@Article{JPDE-17-351, author = {}, title = {Existence and Nonexistence of Global Solutions for Semilinear Heat Equation on Unbounded Domain}, journal = {Journal of Partial Differential Equations}, year = {2004}, volume = {17}, number = {4}, pages = {351--368}, abstract = {

In this paper, we consider the existence and nonexistence of global solutions to the semilinear heat equation u_t - Δu = u^p with Neumann boundary value \frac{∂u}{∂ν} = 0 on some unbounded domains, where p > 1, ν is the outward normal vector on boundary ∂Ω. We prove that there exists a critical exponent p_c = p_c(Ω) > 1 such that if p ∈ (1, p_c], for nonnegative and nontrivial initial data, all positive solutions blow up in finite time; if p > p_c, for suitably small nonnegative initial data, there exists a global positive solution.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5398.html} }
TY - JOUR T1 - Existence and Nonexistence of Global Solutions for Semilinear Heat Equation on Unbounded Domain JO - Journal of Partial Differential Equations VL - 4 SP - 351 EP - 368 PY - 2004 DA - 2004/11 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5398.html KW - Semilinear heat equation KW - global existence KW - critical exponent of Fu-jita' s type AB -

In this paper, we consider the existence and nonexistence of global solutions to the semilinear heat equation u_t - Δu = u^p with Neumann boundary value \frac{∂u}{∂ν} = 0 on some unbounded domains, where p > 1, ν is the outward normal vector on boundary ∂Ω. We prove that there exists a critical exponent p_c = p_c(Ω) > 1 such that if p ∈ (1, p_c], for nonnegative and nontrivial initial data, all positive solutions blow up in finite time; if p > p_c, for suitably small nonnegative initial data, there exists a global positive solution.

Yonggeng Gu & Wenjun Sun . (2019). Existence and Nonexistence of Global Solutions for Semilinear Heat Equation on Unbounded Domain. Journal of Partial Differential Equations. 17 (4). 351-368. doi:
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