The analyticity of solutions of the heat equation with nonlinear boundary conditions

The problem of the one-dimensional heat equation with nonlinear boundary conditions is studied. One of the objectives of the paper is to study the analyticity of solutions. This objective is achieved after first establishing an exact solution to the problem subject to the boundary and initial conditions which are expressed in functions of fractional powers of their arguments. The solution is given in an infinite series of parabolic cylinder functions and time t, which is shown to be absolutely and uniformly convergent. This solution includes previously known solutions as special cases. The analyticity is then inferred from the established solution.