Quasi-linear equations of mixed type in soil heat transfer problem

Non-local boundary problem for quasi-linear equation of the mixed parabolic-hyperbolic type of the second order in contacting area is studied. Uniqueness and possibility of the solution of this non-local problem by method of integral equations is proved by transformation to the linear equation. It is well known that heat transfer process in soil may by described only by mixed equation with boundary and initial conditions. The description or modeling of such a process is a very difficult problem. This work devoted to investigation of parabolic-hyperbolic equations of second order in mixed domain.