Global weak solutions to the weakly dissipative Degasperis–Procesi equation Original Research Article

The global weak solutions for the Degasperis–Procesi equation with weakly dissipative term are investigated. Provided that u0∈H1(R)u0∈H1(R), View the MathML sourcey0=(1−∂x2)u0∈M(R), View the MathML sourcesuppy0−⊂(−∞,x0) and View the MathML sourcesuppy0+⊂(x0,∞), the existence and uniqueness of global weak solutions for the equation are shown to be true in the space View the MathML sourceWloc1,∞(R+×R)∩Lloc∞(R+;H1(R)).