From 34abbcccadea269b45adee7fec1f63a66d2c27e9 Mon Sep 17 00:00:00 2001
From: Tristan Montoya <montoya.tristan@gmail.com>
Date: Sat, 5 Oct 2024 01:42:07 +0200
Subject: [PATCH] fix docs typos

---
 src/ConservationLaws/burgers.jl                    | 6 +++---
 src/ConservationLaws/linear_advection_diffusion.jl | 4 ++--
 2 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/ConservationLaws/burgers.jl b/src/ConservationLaws/burgers.jl
index afd47bc5..5246e66c 100644
--- a/src/ConservationLaws/burgers.jl
+++ b/src/ConservationLaws/burgers.jl
@@ -3,7 +3,7 @@
 
 Define an inviscid Burgers' equation of the form
 ```math
-\partial_t U(\bm{x},t) + \bm{\nabla} \cdot \big(\tfrac{1}{2}\bm{a} U(\bm{x},t)^2 \big) = 0,
+\partial_t U(\bm{x},t) + \bm{\nabla}_{\bm{x}} \cdot \big(\tfrac{1}{2}\bm{a} U(\bm{x},t)^2 \big) = 0,
 ```
 where $\bm{a} \in \R^d$. A specialized constructor `InviscidBurgersEquation()` is provided for the one-dimensional case with `a = (1.0,)`.
 """
@@ -19,12 +19,12 @@ struct InviscidBurgersEquation{d} <: AbstractConservationLaw{d, FirstOrder, 1}
     end
 end
 
-@doc raw"""x
+@doc raw"""
     ViscousBurgersEquation(a::NTuple{d,Float64}, b::Float64) where {d}
 
 Define a viscous Burgers' equation of the form
 ```math
-\partial_t U(\bm{x},t) + \bm{\nabla} \cdot \big(\tfrac{1}{2}\bm{a} U(\bm{x},t)^2 - b \bm{\nabla} U(\bm{x},t)\big) = 0,
+\partial_t U(\bm{x},t) + \bm{\nabla}_{\bm{x}} \cdot \big(\tfrac{1}{2}\bm{a} U(\bm{x},t)^2 - b \bm{\nabla} U(\bm{x},t)\big) = 0,
 ```
 where $\bm{a} \in \R^d$ and $b \in \R^+$. A specialized constructor `ViscousBurgersEquation(b::Float64)` is provided for the one-dimensional case with `a = (1.0,)`.
 """
diff --git a/src/ConservationLaws/linear_advection_diffusion.jl b/src/ConservationLaws/linear_advection_diffusion.jl
index 6cddb03b..327d8818 100644
--- a/src/ConservationLaws/linear_advection_diffusion.jl
+++ b/src/ConservationLaws/linear_advection_diffusion.jl
@@ -3,7 +3,7 @@
 
 Define a linear advection equation of the form
 ```math
-\partial_t U(\bm{x},t) + \bm{\nabla} \cdot \big( \bm{a} U(\bm{x},t) \big) = 0,
+\partial_t U(\bm{x},t) + \bm{\nabla}_{\bm{x}} \cdot \big( \bm{a} U(\bm{x},t) \big) = 0,
 ```
 with a constant advection velocity $\bm{a} \in \R^d$. A specialized constructor `LinearAdvectionEquation(a::Float64)` is provided for the one-dimensional case.
 """
@@ -23,7 +23,7 @@ end
 
 Define a linear advection-diffusion equation of the form
 ```math
-\partial_t U(\bm{x},t) + \bm{\nabla} \cdot \big( \bm{a} U(\bm{x},t) - b \bm{\nabla} U(\bm{x},t)\big) = 0,
+\partial_t U(\bm{x},t) + \bm{\nabla}_{\bm{x}} \cdot \big( \bm{a} U(\bm{x},t) - b \bm{\nabla} U(\bm{x},t)\big) = 0,
 ```
 with a constant advection velocity $\bm{a} \in \R^d$ and diffusion coefficient $b \in \R^+$. A specialized constructor `LinearAdvectionDiffusionEquation(a::Float64, b::Float64)` is provided for the one-dimensional case.
 """