A Class Of Pseudo-parabolic Equation Boundary Value Problem And Heat Cryptosystem

This paper defines the subsolution and supersolution of its boundary value problem by building the comparative theory of the pseudoparabolic equation, obtains a sufficient condition which guarantees the existence and uniqueness or blow-up of the local classical solution; gives the definition of the equilibrium solution and its stabilization by virtue of the theory of the ordinary differential equation, presents a proof that the equilibrium solution appears stable and the global solution exist and unique. At last, we study the cryptosystem based on analog of Sobolev-Galpern equation, prove this cryptosystem available in theory, device a finite element form with convergence to the problem.