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Existence and uniqueness of radially symmetric self‐similar very singular solutions are proved for the singular diffusion equation with gradient absorption∂   t    u  −   Δ   p    u  +   |   ∇  u    |    q    =  0  ,    i  n    (  0  ,  ∞  )  ×    R    N    ,where 2 N /( N +1)< p <2 and  p /2< q < p − N /( N +1), thereby extending previous results restricted to  q >1.

Existence and uniqueness of very singular solutions for a fast diffusion equation with gradient absorption