Besov Spaces and Self-similar Solutions for Nonlinear Evolution Equations (Journal of Partial Differential Equations, 2006)
In this paper, we establish the existence of global self-similar solutions for the heat and convection-diffusion equations. This we do in some homogeneous Besov spaces using the theory of Besov spaces and the Strichartz estimates. Further, the structure of the self-similar solutions has also been established by using an equivalent norm for Besov spaces.
Keywords: Strichartz estimates; admissible triplet; self-similar solution; Besov spaces; evolution equations; well-posedness