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A new definition of conditional invariance for boundary-value problems (BVPs) is proposed. Its relationship with the definitions given earlier for Lie’s invariance, is shown and a wider applicability is demonstrated via a non-trivial example.The definition is applied to reduction of BVPs with the basic reaction-diffusion-convection equation, which is used in physically and biologically motivated problems. The constrains on the functions arising in the boundary conditions are established and the nonlinear BVPs in question are thus reduced to those based on linear second-order ODEs. Moreover, the exact solution of a nonlinear BVP with zero Neumann conditions is found. 2000 Mathematics Subject Classification: 22E70, 35K60, 35K57

Conditional symmetries for boundary value problems: new definition and its application for nonlinear problems with Neumann conditions