Existence of solutions to time-dependent nonlinear diffusion equations via convex optimization (Q1937012)

The author utilizes the variational approach to time-dependent nonlinear diffusion equations in order to obtain a related convex optimization problem. In the case where the potential function is continuous, coercive, and has polynomial growth, the equivalence result is obtained for these problems. Besides, existence and uniqueness of (weak) solutions are derived. In the case where the potential function is singular, optimization problem admits a solution which is a generalized one to the diffusion equation.