Volterra and Functional Differential Equations

A MODEL RIEMANN PROBLEM FOR VOLTERRA EQUATIONS

J. M. Greenberg

Division of Mathematical and Computer Sciences National Science Foundation Washington, D.C. and Department of Mathematics SUNY - Buffalo Buffalo, New York

Ling Hsiao

Division of Applied Mathematics Brown University Providence, Rhode Island and Department of Mathematics Academia - Sinica of ChinaTaipei, Taiwan

R. C. MacCamy

Department of Mathematics Carnegie - Mellon University Pittsburgh, Pennsylvania

DOI: 10.1201/9781003420026-3

1. INTRODUCTION

We seek functions u (x, t) = σ (x, t), x and t in ℝ, which satisfy the conditions:

$$\frac{d}{dt}{{\displaystyle \int }}_{x_1}^{x_2}u\left(x,t\right)dx=-\left(\sigma \left(x_2,t\right)-\sigma \left(x_1,t\right)\right),t>0$$ (B)

$$\sigma \left(x,t\right)=a($$