In the domain Q={(t, x) : tt0>0, x ∈ ℝN}, we study the following Cauchy problem to the double nonlinear parabolic equation not in divergence form with source or absorption:
(1)
(2)

where k, m ≥ 1, p ≥ 2, 0<q<1, ε=±1, λ, n, β are the given numerical parameters.

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