Local existence of solutions to dissipative nonlinear evolution equations with mixed types Original Research Article

In this paper, we consider the local existence of solutions to the Cauchy problems for the following nonlinear evolution equations with mixed types View the MathML source{ψt=−(1−α)ψ−θx+αψxx,θt=−(1−α)θ+γψx+2ψθx+αθxx, Turn MathJax on with initial data View the MathML source(ψ,θ)(x,0)=(ψ0(x),θ0(x))→(ψ±,θ±),as x→±∞, Turn MathJax on where αα and γγ are positive constants satisfying α<1α<1, γ<α(1−α)γ<α(1−α). Through constructing an approximation solution sequence, we obtain the local existence by using the contraction mapping principle.