Electron. J. Differential Equations, Vol. 2016 (2016), No. 250, pp. 1-20.

Self-similar solutions for a superdiffusive heat equation with gradient nonlinearity

Marcelo Fernandes de Almeida, Arlucio Viana

Abstract:
This article studies the existence, stability, self-similarity and symmetries of solutions for a superdiffusive heat equation with superlinear and gradient nonlinear terms with initial data in new homogeneous Besov-Morrey type spaces. Unlike in previous works on such time-fractional partial differential equations of order $\alpha\in(1,2)$, we take non null initial velocities into consideration, where new difficulties arise from. We overcome them by developing an appropriate decomposition of the two-parametric Mittag-Leffler function to obtain Mikhlin-type estimates and obtain our existence theorem.

Submitted July 8, 2016. Published Septembere 19, 2016.
Math Subject Classifications: 35A01, 35R11, 35R09, 35B06, 35C06, 35K05, 35L05.
Key Words: Fractional partial differential equations; self-similarity; radial symmetry; Sobolev-Morrey spaces.

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Marcelo Fernandes de Almeida
Universidade Federal de Sergipe
DMA - Departamento de Matemática
Avenida Rosa Else, São Cristíovão
Sergipe, Brazil
email: nucaltiado@gmail.com
Arlúcio Viana
Universidade Federal de Sergipe
DMAI - Departamento de Matemática
Avenida Vereador Olíimpio Grande
Itabaiana, Sergipe, Brazil
email: arlucioviana@ufs.br

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