Boundary value problem for a nonlinear equation of mixed type

In this paper, we consider the boundary value problem for a nonlinear Lavrentiev-Bitsadze equation of mixed type partial derivative(2)(u) over cap/partial derivative x(2) + (sgn y)(1 + (u) over cap (2)(x)) partial derivative(2)(u) over cap/partial derivative y(2) = 0, whose coefficients depend on the first order derivatives of unknown function. Above y = 0 and below y = 0, the equation becomes the nonlinear elliptic equation and nonlinear hyperbolic, equation respectively, this is different from the equation studied in Chen (2011) [9]. We prove the existence of solution to the problem by the method which can be used to study more difficult problems for nonlinear equations of mixed type arising in gas dynamics. (C) 2013 Elsevier Inc. All rights reserved.