Evolution equations in generalized Stepanov-like pseudo almost automorphic spaces
In this article, first we introduce and study the concept of $mathbb{S}_{gamma}^p$-pseudo almost automorphy (or generalized Stepanov-like pseudo almost automorphy), which is more general than the notion of Stepanov-like pseudo almost automorphy due to Diagana. We next study the existence of solu...
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| Format: | Article |
| Language: | English |
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Texas State University
2012-03-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/49/abstr.html |
| Summary: | In this article, first we introduce and study the concept of $mathbb{S}_{gamma}^p$-pseudo almost automorphy (or generalized Stepanov-like pseudo almost automorphy), which is more general than the notion of Stepanov-like pseudo almost automorphy due to Diagana. We next study the existence of solutions to some classes of nonautonomous differential equations of Sobolev type in $mathbb{S}_{gamma}^p$-pseudo almost automorphic spaces. To illustrate our abstract result, we will study the existence and uniqueness of a pseudo almost automorphic solution to the heat equation with a negative time-dependent diffusion coefficient. |
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| ISSN: | 1072-6691 |