On the Heat Equation with Nonlinear and Nonlocal Boundary Conditions

This paper deals with some theoretical results concerning a heat equation with certain nonlinear and nonlocal boundary conditions. An equivalent system of nonlinear Volterra integral equations is set up and the existence and uniqueness of the solution of the original problem are demonstrated on [0, ∞) through the existence and uniqueness of the solution of the Volterra integral equation system. In addition, the asymptotic behavior of the solution as t → 0 and t → ∞ is obtained and other properties of the solution, e.g., monotonicity, are investigated.