Introduction

This book focuses on control problems for conservation laws, i.e., equations of the type: ∂tu+∂xf(u)=0ut+(f(u))x=0,$$\displaystyle  \partial _t\, u + \partial _x\, f(u) = 0 \qquad  u_t+(f(u))_x=0,  $$where u:ℝ+×ℝ→ℝn$$u:\mathbb {R}^+\times \mathbb {R} \to \mathbb {R}^n$$is the vector of conserved quantities and f:ℝn→ℝn$$f:\mathbb {R}^n\to \mathbb {R}^n$$is the flux. Most results will be given for the scalar case (n = 1), but we will present few results valid in the general case.