In order to become worldly things, that is, deeds and facts and events and patterns of
thoughts or ideas,[action, speech, and thought] must first be seen, heard, and remembered …

We consider an abstract second order linear equation with a strong dissipation, namely a
friction term which depends on a power of the “elastic” operator. In the homogeneous case …

We consider a diffusion problem on a network on whose nodes we impose Dirichlet and
generalized, non-local Kirchhoff-type conditions. We prove well-posedness of the …

We consider a linear system of PDEs of the form 1 & u_ tt-c Δ u_t-Δ u &= 0\quad
in\varOmega * (0, T)\u_ tt+\partial_n (u+ cu_t)-\Delta_\varGamma (c α u_t+ u) &= 0\quad …

The contraction semigroup S (t)= e^ t AS (t)= et A generated by the abstract linear dissipative
evolution equation ̈ u+ A u+ f (A) ̇ u= 0 u¨+ A u+ f (A) u˙= 0 is analyzed, where A is a …

The goal of this paper is to study the Cauchy problem for a family of structural damped
models interpolation between classical damped wave and wave model with viscoelastic …

We study higher-order elliptic operators on one-dimensional ramified structures (networks).
We introduce a general variational framework for fourth-order operators that allows us to …

In this paper we study a substantial generalization of the model of excited random walk
introduced in Electron. Commun. Probab. 8 (2003) 86–92 by Benjamini and Wilson. We …

We consider elliptic operators with operator-valued coefficients and discuss the associated
parabolic problems. The unknowns are functions with values in a Hilbert space W. The …

We establish a new method for obtaining nonconvex spectral enclosures for operators
associated with second‐order differential equations in a Hilbert space. In particular, we …