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On a third order parabolic equation with a nonlocal boundary condition. (English) Zbl 0959.35082
Summary: 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.

MSC:
35K35 Initial-boundary value problems for higher-order parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B45 A priori estimates in context of PDEs
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