diff --git a/Project.toml b/Project.toml
index 61b1bdc..a5240a9 100644
--- a/Project.toml
+++ b/Project.toml
@@ -24,6 +24,7 @@ NonlinearSolve = "3, 4"
 OptimizationOptimJL = "0.3, 0.4"
 OrdinaryDiffEq = "6.80.0, 7"
 OrdinaryDiffEqSDIRK = "1.2.0, 2"
+Random = "1"
 SafeTestsets = "0.1"
 SciMLBase = "2.69.0, 3.1"
 SciMLTesting = "1"
diff --git a/lib/linear_convection.jl b/lib/linear_convection.jl
index 587f276..92e100f 100644
--- a/lib/linear_convection.jl
+++ b/lib/linear_convection.jl
@@ -488,7 +488,7 @@ function trans_sin()
     bcs = [
         u(0, z) ~ u_exact(0, z),
         u(t, 0) ~ u_exact(t, 0),
-        (t, 2π) ~ u_exact(t, 2π),
+        u(t, 2π) ~ u_exact(t, 2π),
     ]
 
     # Space and time domains
@@ -506,7 +506,7 @@ function trans_sin()
     # PDESystem
 
     @named trans_sin = PDESystem(
-        eqs, bcs, domains, [t, z], [u(t, z)], analytic = ref,
+        eq, bcs, domains, [t, z], [u(t, z)], analytic = ref,
         metadata = tags
     )
 
diff --git a/test/qa/qa.jl b/test/qa/qa.jl
index d77c55b..2c50f5d 100644
--- a/test/qa/qa.jl
+++ b/test/qa/qa.jl
@@ -1,5 +1,14 @@
 using PDESystemLibrary, Aqua, JET
 using SciMLTesting
 
-run_qa(PDESystemLibrary; Aqua = Aqua, JET = JET, jet = true,
-    jet_kwargs = (; target_defined_modules = true))
+# JET runs in `:typo` mode (the SciMLTesting `run_qa` default). The library's
+# problem builders construct symbolic expressions from `@variables`/`@parameters`;
+# `Symbolics.wrap` has a union return type that JET widens to include the callable
+# wrapper `Symbolics.CallAndWrap` (only produced by `@variables u(..)`), so basic-mode
+# analysis emits spurious `no matching method found` union-split reports for `+/-/*/cos/sin`
+# on scalar variables that are always `Num` at runtime. Typo mode still catches real
+# undefined-name errors without these dependency-inference false positives.
+run_qa(
+    PDESystemLibrary; Aqua = Aqua, JET = JET, jet = true,
+    jet_kwargs = (; target_modules = (PDESystemLibrary,), mode = :typo)
+)