Coerciveness of the discontinuous initial-boundary value problem for parabolic equations

Some Spectral Properties of One Sturm-Liouville Type Problem with Discontinuous Weight

“…Note that in [12][13][14][15] such properties as isomorphism, coerciveness with respect to the spectral parameter, completeness of root functions, distributions of eigenvalues of some discontinuous boundary value problems with transmission conditions and its applications to the corresponding initial-boundary value problems for parabolic equations there were studied.…”

Discontinuous Sturm–Liouville Problems with Eigenparameter-Dependent Boundary and Transmissions Conditions

“…For example, some boundary-value problems with transmission conditions arise in heat and mass transfer problems (see, for example, [4]), in vibrating string problems when the string loaded additionally with point masses (see, for example, [12]) and in diffraction problems (see,for example, [15]). Properties such as isomorphism, coerciveness with respect to the spectral parameter, completeness and Abel bases of a system of root functions, distributions of eigenvalues of some discontinuous boundary value problems with transmission conditions and its applications to the corresponding initial-boundaryvalue problems for parabolic equations have been investigated in [5][6][7][8]14] and [17]. Also, some problems with transmission conditions which arise in mechanics (thermal conduction problem for a thin laminated plate) were studied in the article [14].…”

Solvability and coerciveness of multi-point Sturm–Liouville problems with abstract linear functionals

“…Note that an abstract theory of the boundary value problems with continuous coefficients and an eigenvalue parameter in the boundary conditions have been constructed by Yakubov and Yakubov (see [4] and corresponding bibliography). Many authors have been devoted to the study of discontinuous problems [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. To deal with the discontinuity of the problem, transmission conditions are imposed on the discontinuous points.…”

“…[18,23]. The properties of isomorphism, Fredholmness, and coerciveness of Sturm-Liouville problems with one discontinuous point were investigated by Mukhtarov and his coauthors in [6,8,9,24].…”