On a mixed problem with integral conditions for one-dimensional parabolic equation

Abstract

We consider an initial-boundary value problem for a one-dimensional parabolic equation with nonlocal boundary conditions. These nonlocal conditions are given in terms of integrals. Based on solution of the Dirichlet problem for the parabolic equation, we constructively establish the well-posedness for the nonlocal problem.

†Dedicated to Professor Wei Lin on the occasion of his 70th birthday.

Keywords:

• Parabolic equation
• Nonlocal boundary conditions
• Volterra integral equation
• Dirichlet problem
• Semigroup

Keywords:

• AMS subject classifications: 35K15
• 35K20

Acknowledgement

This work is partly supported by NSF of China, NSF of GuangDong.

Notes

†Dedicated to Professor Wei Lin on the occasion of his 70th birthday.