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We investigate the well-posedness of a class of nonlinear dispersive waves on trees, in connection with the mathematical modeling of the human cardiovascular system. Specifically, we study the Benjamin-Bona-Mahony (BBM) equation, also known as the regularized long wave equation, posed on finite trees, together with standard junction and terminal boundary… (More)

- RADU CASCAVAL
- 2008

In this note we prove that the maximally defined operator associated with the Dirac-type differential expression M(Q) = i ( d dx Im −Q −Q − d dx Im ) , where Q represents a symmetric m × m matrix (i.e., Q(x) = Q(x) a.e.) with entries in L loc (R), is J -self-adjoint, where J is the antilinear conjugation defined by J = σ1C, σ1 = ( 0 Im Im 0 ) and C(a1, . .… (More)

- Radu C. Cascaval
- Mathematics and Computers in Simulation
- 2012

We derive a nonlinear model for the pressure and flow velocity wave propagation in an arterial segment. We then study the transmission and reflection of pulses at bifurcation. We observe a linear dependence of the transmitted speeds to the incoming speeds, and similarly for the reflected speeds. We propose a method for validating the numerical results… (More)

- Radu C Cascaval, Ciro D'Apice, Maria Pia D'Arienzo, Rosanna Manzo
- Mathematical biosciences and engineering : MBE
- 2017

The development of mathematical models for studying phenomena observed in vascular networks is very useful for its potential applications in medicine and physiology. Detailed 3D studies of flow in the arterial system based on the Navier-Stokes equations require high computational power, hence reduced models are often used, both for the constitutive laws and… (More)

- V. Batchenko, V. Borovyk, +9 authors Vita Borovyk
- 2003

We revisit the computation of (2-modified) Fredholm<lb>determinants for operators with matrix-valued semi-separable inte-<lb>gral kernels. The latter occur, for instance, in the form of Green’s<lb>functions associated with closed ordinary differential operators on<lb>arbitrary intervals on the real line. Our approach determines the<lb>(2-modified) Fredholm… (More)

We study Darboux-type transformations associated with the focusing nonlinear Schrödinger equation (NLS−) and their effect on spectral properties of the underlying Lax operator. The latter is a formally J -selfadjoint (but non-self-adjoint) Dirac-type differential expression of the form M(q) = i d dx −q −q − d dx , satisfying JM(q)J = M(q), where J is… (More)

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