The Lindblad Equation, named after Goran Lindblad, generalizes Schrödinger's equation to the case of dissipation, i.e., bringing in damping, decoherence, etc. $$i\hbar\partial_t\rho=\mathcal{L}\rho$$ where $$\mathcal{L}\equiv[H,\rho] + i\hbar\sum_k \gamma_k\left(L_k\rho L_k^\dagger - \frac{1}{2}\{L_k^\dagger L_k,\rho\}\right),$$ with $\gamma_k \ge 0$. This is the most general form of an equation that satisfies the properties needed for $\rho$ to remain a physical density matrix.
Some people call it the GKSL (for Gorini–Kossakowski–Sudarshan[1] and Lindblad[2]) equation. Lindblad's derivation covers the general (including infinite-dimensional) case using completely positive maps; GKS covers the finite $N$-level case, published simultaneously and independently. Earlier works exist.[3][4]