On nonlocal boundary value problems for hyperbolic-parabolic equations

Abstract

The nonlocal boundary value problem for hyperbolic-parabolic equationsfor differential equation in a Hilbert space H, with the self-adjoint positive definite operator A is considered. The stability estimates for the solution of this problem are established. In applications, the stability estimates for the solutions of the mixed type boundary value problems for hyperbolic-parabolic equations are obtained.

The hyperbolic-elliptic equation with the nonlocal condition

“…Using the last formula and the estimates (3), (4), (5) and (6), we can obtain Now, we will obtain the same estimates for the norm of u.t/, A 1=2 u.t/ and Au.t/. Using the identities (13) and (14) and the estimates (3), (4), (5), (6), we obtain…”

“…1/ H . Applying A 1=2 to the identity (15) and using the estimates (3), (4), (5) and (6), in a similar manner, we obtain…”

“…They also play a very important role for mathematical modelling in many branches of science, engineering and industry. Theory and numerical methods of solutions of the boundary value problems endowed with the local and nonlocal boundary conditions for partial differential equations have been investigated by many researchers ( [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and the references therein).…”

On stable implicit difference scheme for hyperbolic–parabolic equations in a Hilbert space

“…In the article [3], the stability estimates for the solution of problem (1.1) are established. In applications, the stability estimates for solutions of mixed type boundary value problems for hyperbolic-parabolic equations are obtained.…”

Second Order Equations in Functional Spaces: Qualitative and Discrete Well-Posedness

“…The generalization of stability estimates results of [82,83] was presented in [84,85] for the solution of the multipoint nonlocal boundary value problem…”