For nonlinear singular first-order PDEs t du/dt = F(t,x,u,du/dx) with Re lambda(0,0) < 0, the double-limit condition (2.3) forces any local solution to coincide with the distinguished solution u0, yielding uniqueness and analytic continuation criteria.
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Uniqueness of the solution of nonlinear singular first order partial differential equations
For nonlinear singular first-order PDEs t du/dt = F(t,x,u,du/dx) with Re lambda(0,0) < 0, the double-limit condition (2.3) forces any local solution to coincide with the distinguished solution u0, yielding uniqueness and analytic continuation criteria.