Well-posedness for the Cauchy problem of spatially weighted dissipative   equation
  This paper mainly investigates the Cauchy problem of the spatially weighted dissipative equation with initial data in the weighted Lebesgue space. A generalized Hankel Transform is introduced to derive the analytical solution and a special Young's Inequality has been applied to prove the space-time estimates for this type of equation. 
Ziheng Tu and Xiaojun Lu
math.AP