In this paper we give new derivations of the heat and wave equation which incorporate the
boundary conditions into the formulation of the problems. The principle of least action and …

For a symmetric operator or relation A with infinite deficiency indices in a Hilbert space we
develop an abstract framework for the description of symmetric and self-adjoint extensions …

In this note we introduce a general framework which allows us to prove in a unified and
systematic way that operators with Wentzell-type boundary conditions generate analytic …

We present an analysis of regularity and stability of solutions corresponding to wave
equation with dynamic boundary conditions. It has been known since the pioneering work by …

In this paper, we study a basic generation problem concerning the second order differential
operator ad2dx2+ bddx+ c in the space C [0, 1] of complex continuous functions equipped …

Au+ β∂ u∂ ν+ γu= 0 on∂ Ω,(1.1) where ν is the outer unit normal, and the boundary∂ Ω is
C2. Under the assumption that a=(aij)=(αδij)(here δij stands for the identity matrix in Rn) is a …

In this article, we introduce and investigate bi-continuous cosine families. Those are inspired
by the theory of bi-continuous semigroups which had an impact in the area of evolution …

Let a∈ W1,∞(0, 1), a (x)⩾ δ> 0, b, c∈ L∞(0, 1) and consider the differential operator A
formally given by Au= au ″+ bu′+ cu. We prove in the first part that a realization of A with …

We show that generation theorems for cosine families related to one-dimensional
Laplacians in C [0,∞] may be obtained by Lord Kelvin's method of images, linking them with …

Let a∈ W 1,∞(0, 1), a (x)≥ α> 0, b, c∈ L∞(0, 1) and consider the differential operator A
given by Au= au ″+ bu′+ cu. Let α j, β j (j= 0, 1) be complex numbers satisfying α j, β j≠(0 …