Approximate controllability for the semilinear heat equation in R N involving gradient terms
We prove the approximate controllability of the semilinear heat equation in R N, when the nonlinear term is globally Lipschitz and depends both on the state u and its spatial gradient <FONT FACE=Symbol>Ñ</FONT>u. The approximate controllability is viewed as the limit of a sequence of optimal control problems. In order to avoid the difficulties related to the lack of compactness of the Sobolev embeddings, we work with the similarity variables and use weighted Sobolev spaces.
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| Format: | Digital revista |
| Language: | English |
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Sociedade Brasileira de Matemática Aplicada e Computacional
2003
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| Online Access: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022003000100008 |
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| Summary: | We prove the approximate controllability of the semilinear heat equation in R N, when the nonlinear term is globally Lipschitz and depends both on the state u and its spatial gradient <FONT FACE=Symbol>Ñ</FONT>u. The approximate controllability is viewed as the limit of a sequence of optimal control problems. In order to avoid the difficulties related to the lack of compactness of the Sobolev embeddings, we work with the similarity variables and use weighted Sobolev spaces. |
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