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

This paper is devoted to global well-posedness, 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 the heat equation, we need to develop an appropriate deco...

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Bibliographic Details
Published in:arXiv.org 2016-05
Main Authors: Fernandes de Almeida, Marcelo, Arlúcio da Cruz Viana
Format: Article
Language:English
Subjects:
Brownian motion
Nonlinearity
Partial differential equations
Self-similarity
Thermodynamics
Well posed problems
Online Access:Get full text
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Summary:This paper is devoted to global well-posedness, 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 the heat equation, we need to develop an appropriate decomposition of the two-parametric Mittag-Leffler function in order to obtain Mikhlin-type estimates get our well-posedness theorem. To the best of our knowledge, the present work is the first one concerned with a well-posedness theory for a time-fractional partial differential equations of order \(\alpha\in(1,2)\) with non null initial velocity.
ISSN:2331-8422