## Taiwanese Journal of Mathematics

### ON NONLOCAL BOUNDARY VALUE PROBLEMS FOR HYPERBOLIC-PARABOLIC EQUATIONS

#### Abstract

The nonlocal boundary value problem for hyperbolic-parabolic equations $\left\{ \!\! \begin{array}{c} \frac{d^{2}u(t)}{dt^{2}}+Au(t)=f(t)(0\leq t\leq 1),\frac{du(t)}{dt} +Au(t)=g(t)(-1\leq t\leq 0), \\ u(-1)\!=\!\sum\limits_{i=1}^{N}\alpha _{i}u\left( \mu _{i}\right) \!+\!\sum\limits_{i=1}^{L}\beta _{i}u^{\prime }\left( \lambda _{i}\right) \!+\!\varphi ,\sum\limits_{i=1}^{N}|\alpha _{i}|,\sum\limits_{i=1}^{L}\left\vert \beta _{i}\right\vert \leq 1,0\!\lt \!\mu _{i},\lambda _{i}\!\leq\! 1 \end{array} \right.$ for 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 bundary value problems for hyperbolic-parabolic equations are obtained.

#### Article information

Source
Taiwanese J. Math., Volume 11, Number 4 (2007), 1075-1089.

Dates
First available in Project Euclid: 18 July 2017