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
,
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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