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Semilinear parabolic equations with superlinear reaction terms, and application to some convection-diffusion problems
We are interested in the existence of distributional solutions for two types of nonlinear evolution problems, whose models are (1.1) and (1.2) below. In the first one the nonlinear reaction term depends on the solution with a slightly superlinear growth. In the second one we consider a first order t...
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Інститут прикладної математики і механіки НАН України
2004
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| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/124629 |
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irk-123456789-1246292017-10-01T03:02:56Z Semilinear parabolic equations with superlinear reaction terms, and application to some convection-diffusion problems Dall'Aglio, A. Giachett, D. Segura de Leon, S. We are interested in the existence of distributional solutions for two types of nonlinear evolution problems, whose models are (1.1) and (1.2) below. In the first one the nonlinear reaction term depends on the solution with a slightly superlinear growth. In the second one we consider a first order term depending also on the gradient of the solution in a quadratic way. The two problems are strictly related from the point of view of the a priori estimates we can obtain on their solutions. We point out that no boundedness is assumed on the data of the problems. This implies that the methods involving sub/super-solutions do not apply, and we have to use some convenient test-function to prove the a priori estimates. 2004 Article Semilinear parabolic equations with superlinear reaction terms, and application to some convection-diffusion problems / A. Dall'Aglio, D. Giachett, S. Segura de Leon // Український математичний вісник. — 2004. — Т. 1, № 4. — С. 518-531. — Бібліогр.: 13 назв. — англ. 1810-3200 2000 MSC. 35B33, 35B45, 35K20, 35K55, 35K57. http://dspace.nbuv.gov.ua/handle/123456789/124629 en Український математичний вісник Інститут прикладної математики і механіки НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| description |
We are interested in the existence of distributional solutions for two types of nonlinear evolution problems, whose models are (1.1) and (1.2) below. In the first one the nonlinear reaction term depends on the solution with a slightly superlinear growth. In the second one we consider a first order term depending also on the gradient of the solution in a quadratic way. The two problems are strictly related from the point of view of the a priori estimates we can obtain on their solutions. We point out that no boundedness is assumed on the data of the problems. This implies that the methods involving sub/super-solutions do not apply, and we have to use some convenient test-function to prove the a priori estimates. |
| format |
Article |
| author |
Dall'Aglio, A. Giachett, D. Segura de Leon, S. |
| spellingShingle |
Dall'Aglio, A. Giachett, D. Segura de Leon, S. Semilinear parabolic equations with superlinear reaction terms, and application to some convection-diffusion problems Український математичний вісник |
| author_facet |
Dall'Aglio, A. Giachett, D. Segura de Leon, S. |
| author_sort |
Dall'Aglio, A. |
| title |
Semilinear parabolic equations with superlinear reaction terms, and application to some convection-diffusion problems |
| title_short |
Semilinear parabolic equations with superlinear reaction terms, and application to some convection-diffusion problems |
| title_full |
Semilinear parabolic equations with superlinear reaction terms, and application to some convection-diffusion problems |
| title_fullStr |
Semilinear parabolic equations with superlinear reaction terms, and application to some convection-diffusion problems |
| title_full_unstemmed |
Semilinear parabolic equations with superlinear reaction terms, and application to some convection-diffusion problems |
| title_sort |
semilinear parabolic equations with superlinear reaction terms, and application to some convection-diffusion problems |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2004 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/124629 |
| citation_txt |
Semilinear parabolic equations with superlinear reaction terms, and application to some convection-diffusion problems / A. Dall'Aglio, D. Giachett, S. Segura de Leon // Український математичний вісник. — 2004. — Т. 1, № 4. — С. 518-531. — Бібліогр.: 13 назв. — англ. |
| series |
Український математичний вісник |
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AT dallaglioa semilinearparabolicequationswithsuperlinearreactiontermsandapplicationtosomeconvectiondiffusionproblems AT giachettd semilinearparabolicequationswithsuperlinearreactiontermsandapplicationtosomeconvectiondiffusionproblems AT seguradeleons semilinearparabolicequationswithsuperlinearreactiontermsandapplicationtosomeconvectiondiffusionproblems |
| first_indexed |
2023-10-18T20:46:48Z |
| last_indexed |
2023-10-18T20:46:48Z |
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1796151088905191424 |