Abdelfatah Bouziani, "On a third order parabolic equation with a nonlocal boundary condition", International Journal of Stochastic Analysis, vol. 13, Article ID 217058, 15 pages, 2000. https://doi.org/10.1155/S1048953300000198
On a third order parabolic equation with a nonlocal boundary condition
In this paper we demonstrate the existence, uniqueness and continuous dependence of a strong solution upon the data, for a mixed problem which combine classical boundary conditions and an integral condition, such as the total mass, flux or energy, for a third order parabolic equation. We present a functional analysis method based on an a priori estimate and on the density of the range of the operator generated by the studied problem.
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