On the role of the Besov spaces for the solutions of the generalized burgers equation in homogeneous Sobolev spaces Original Research Article

The generalized Burgers equation ∂tu−∂xxu+∂xuk+1=0, with initial data u0 in homogeneous Sobolev spaces are investigated. The starting point of this work is the construction of solutions in View the MathML source for small size initial data in View the MathML source. If in addition, the initial data belongs to View the MathML source then the obtained solution is actually in View the MathML source.