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 types {psi(t) = -(1 - alpha)psi - theta(x) + alpha psi(xx), theta(t) = -(1 - alpha)theta + gamma psi(x) + 2 psi theta(x) + alpha theta(xx), with initial data (psi, theta)(x, 0) = (psi(0)(x), theta(0)(x)) -> (psi(+/-), theta(+/-)), as x -> +/-infinity, where alpha and gamma are positive constants satisfying alpha < 1, gamma < alpha(1 - alpha). Through constructing an approximation solution sequence, we obtain the local existence by using the contraction mapping principle. (C) 2009 Elsevier Ltd. All rights reserved.