Spectral properties of a Frankl type problem for parabolic-hyperbolic equations

Abstract

In this article we study spectral properties of non-local boundary-value problem for an equation of parabolic-hyperbolic type. The non-local condition binds the solution values at points on boundaries of the parabolic and hyperbolic parts of the domain with each other. Nonlocal boundary conditions of such type are called Frankl-type conditions. This problem was first formulated by Kal'menov and Sadybekov who proved the unique strong solvability. In this article we investigate one particular case of this problem, for which we show that the problem does not have eigenvalues.

Keywords

• Equation of the mixed type
• parabolic-hyperbolic equation
• Non-local boundary value problem
• Frankl type problem
• spectral properties
• eigenvalues