Definition 2.6.3.label Let $E$ be a Banach space, $A: E \to E$ be a densely defined, closed operator, then $A$ is dissipative if for every $x \in E$, there exists $\phi \in E^{*}$ such that:

1. (1)

   $\norm{\phi}_{E^*}= \norm{x}_{E}$.

2. (2)

   $\dpb{x, \phi}{E}= \norm{x}_{E}^{2}$.

3. (3)

   $\phi(Ax) \le 0$.