Differential and Integral Equations

Self-similarity, symmetries and asymptotic behavior in Morrey spaces for a fractional wave equation

Lucas C.F. Ferreira and Marcelo Fernandes de Almeida

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This paper is concerned with a fractional PDE that interpolates semilinear heat and wave equations. We show results on global-in-time well-posedness for small initial data in the critical Morrey spaces and space dimension $n\geq1$. We also remark how to derive the local-in-time version of the results. Qualitative properties of solutions like self-similarity, antisymmetry and positivity are also investigated. Moreover, we analyze the asymptotic stability of the solutions and obtain a class of asymptotically self-similar solutions.

Article information

Differential Integral Equations, Volume 25, Number 9/10 (2012), 957-976.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 35R11: Fractional partial differential equations 35R09: Integro-partial differential equations [See also 45Kxx] 35A01: Existence problems: global existence, local existence, non-existence 35C15: Integral representations of solutions 35B06: Symmetries, invariants, etc. 35C06: Self-similar solutions 35B40: Asymptotic behavior of solutions 42B35: Function spaces arising in harmonic analysis 35K05: Heat equation 35L05: Wave equation 26A33: Fractional derivatives and integrals


de Almeida, Marcelo Fernandes; Ferreira, Lucas C.F. Self-similarity, symmetries and asymptotic behavior in Morrey spaces for a fractional wave equation. Differential Integral Equations 25 (2012), no. 9/10, 957--976. https://projecteuclid.org/euclid.die/1356012377

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