Blow-up for a semilinear heat equation with moving nonlinear reaction
We study the behavior of solutions of the semilinear problem $$\displaylines{ u_t=u_{xx}+(1+(T-t)^{-\alpha}\chi_{\{|x|<(T-t)^{1/2}\}}) u^p,\quad x\in\mathbb R,\; t\in(0,T),\cr u(x,0)=u_0(x)\ge 0, \quad x\in\mathbb R, }$$ with $\alpha>0$ and p>0 We describe, in terms of the parameters...
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| Format: | Article |
| Language: | English |
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Texas State University
2018-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2018/32/abstr.html |
| _version_ | 1819128213274624000 |
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| author | Raul Ferreira |
| author_facet | Raul Ferreira |
| author_sort | Raul Ferreira |
| collection | DOAJ |
| description | We study the behavior of solutions of the semilinear problem
$$\displaylines{
u_t=u_{xx}+(1+(T-t)^{-\alpha}\chi_{\{|x|<(T-t)^{1/2}\}}) u^p,\quad
x\in\mathbb R,\; t\in(0,T),\cr
u(x,0)=u_0(x)\ge 0, \quad x\in\mathbb R,
}$$
with $\alpha>0$ and p>0 We describe, in terms of the parameters when the
solution is bounded and when it blows up. For blowing up solutions we find
the blow-up rate and the blow-up set. |
| first_indexed | 2024-12-22T08:24:15Z |
| format | Article |
| id | doaj.art-94419f6cf6c040dc8fe1844fa12a0799 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-22T08:24:15Z |
| publishDate | 2018-01-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-94419f6cf6c040dc8fe1844fa12a07992022-12-21T18:32:40ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912018-01-01201832,111Blow-up for a semilinear heat equation with moving nonlinear reactionRaul Ferreira0 Univ. Complutense de Madrid, Spain We study the behavior of solutions of the semilinear problem $$\displaylines{ u_t=u_{xx}+(1+(T-t)^{-\alpha}\chi_{\{|x|<(T-t)^{1/2}\}}) u^p,\quad x\in\mathbb R,\; t\in(0,T),\cr u(x,0)=u_0(x)\ge 0, \quad x\in\mathbb R, }$$ with $\alpha>0$ and p>0 We describe, in terms of the parameters when the solution is bounded and when it blows up. For blowing up solutions we find the blow-up rate and the blow-up set.http://ejde.math.txstate.edu/Volumes/2018/32/abstr.htmlSemilinear parabolic equationblow-upasymptotic behaviour |
| spellingShingle | Raul Ferreira Blow-up for a semilinear heat equation with moving nonlinear reaction Electronic Journal of Differential Equations Semilinear parabolic equation blow-up asymptotic behaviour |
| title | Blow-up for a semilinear heat equation with moving nonlinear reaction |
| title_full | Blow-up for a semilinear heat equation with moving nonlinear reaction |
| title_fullStr | Blow-up for a semilinear heat equation with moving nonlinear reaction |
| title_full_unstemmed | Blow-up for a semilinear heat equation with moving nonlinear reaction |
| title_short | Blow-up for a semilinear heat equation with moving nonlinear reaction |
| title_sort | blow up for a semilinear heat equation with moving nonlinear reaction |
| topic | Semilinear parabolic equation blow-up asymptotic behaviour |
| url | http://ejde.math.txstate.edu/Volumes/2018/32/abstr.html |
| work_keys_str_mv | AT raulferreira blowupforasemilinearheatequationwithmovingnonlinearreaction |