Coercive boundary value problems for parabolic overdetermined systems with variable coefficients
One denotes by \((A,B)\) the boundary value problem operator \[ (A,B): {\mathcal E}(E_ 0')\to {\mathcal E}(E_ 1')\times {\mathcal E}(G_ 1') \] where \(B: y\to (B_ 1y)|_{\Gamma}\), and A and \(B_ 1\) are differential operators. If M is a smooth manifold with smooth boundary \(\Gamma\), \(\dim M=n\) and \(E_ i\), \(G_ i\) smooth finite dimensional vector fiberings on M respectively on \(\Gamma\), then \(E_ i'\) and \(G_ i'\) are their inverse images and \({\mathcal E}(E_ i')\), \({\mathcal E}(G_ i')\) are spaces of \(C^{\infty}\) smooth sections of fiberings \(E_ i'\) and \(G_ i'\). One denotes \(M'=M\times R^ 1\) and \(\Gamma '=\Gamma \times R^ 1\). For the operator (A,B) with the coefficients depending upon t, one builds an \(\partial-\gamma\) joint operator and one proves the solvability of the coercive boundary value problem, with the fulfillment of the compatibility condition on the finite and infinite interval in t.
scientific article; zbMATH DE number 4059972