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A Second-Order Evolution Equation and Logarithmic Operators

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Abstract

In this paper we introduce a matrix representation of the logarithmic wave operator and we study a second-order semilinear evolution equation governed by this operator. We present a result of local well-posedness for this problem and properties of the logarithmic wave operator in terms of the logarithmic negative Dirichlet Laplacian operator.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa, PB, 58051-900, Brazil

    F. D. M. Bezerra

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  1. F. D. M. Bezerra
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Correspondence to F. D. M. Bezerra.

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Bezerra, F.D.M. A Second-Order Evolution Equation and Logarithmic Operators. Bull Braz Math Soc, New Series 53, 571–593 (2022). https://doi.org/10.1007/s00574-021-00271-8

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  • DOI: https://doi.org/10.1007/s00574-021-00271-8

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