International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 4, Pages 201-213
doi:10.1155/S0161171202005860

On the solvability of parabolic and hyperbolic problems with a boundary integral condition

Abstract

We prove the existence, uniqueness, and the continuous dependence of a generalized solution upon the data of certain parabolic and hyperbolic equations with a boundary integral condition. The proof uses a functional analysis method based on a priori estimates established in nonclassical function spaces, and on the density of the range of the linear operator associated to the abstract formulation of the studied problem.