Local Existence Of Solutions To Dissipative Nonlinear Evolution Equations With Mixed Types

In this paper, we consider the local existence of solutions to the Cauchy problems for the following nonlinear evolution equations with mixed typeswith initial data(ψ,θ)(x,0)=(ψ₀(x),θ₀(x))→(ψ_±,θ_±),as x→±∞,whereαandγare positive constants satisfyingα< 1,γ<α(1-α). Through constructing an approximation solution sequence, we obtain the local existence by using the contraction mapping principle.