Classical and weak solutions of the partial differential equations associated with a class of two-point boundary value problems

Abstract

Abstract This paper is concerned with a kind of first-order quasilinear parabolic partial differential equations associated with a class of ordinary differential equations with two-point boundary value problems. We prove that the function given by the solution of an ordinary differential equation is the unique solution of a first-order quasilinear parabolic partial differential equation in both classical and weak senses.

Keywords

• Two-point boundary value problems
• Ordinary differential equations
• Quasilinear partial differential equations
• Sobolev weak solutions
• Viscosity solutions