5 papers
On generalised d'Alembert-type integral representations for damped wave equations on the quarter-plane
Andreas Chatziafratis, Claudio Giorgi, Alain Miranville +1
We rigorously construct and verify a posteriori new closed-form solutions for the forced Maxwell-Cattaneo-Vernotte equation (also broadly known as the damped wave equation, hyperbo…
The linear Cahn-Hilliard equation with an interface
Andreas Chatziafratis, Alain Miranville, Tohru Ozawa
We obtain new integral representations, expressed as contour integrals in the complex Fourier plane, for the solution of fully nonhomogeneous interface problems for the linearized…
Higher-order diffusion and Cahn-Hilliard-type models revisited on the half-line
A. Chatziafratis, A. Miranville, G. Karali +2
In this paper, we solve explicitly and analyze rigorously inhomogeneous initial-boundary-value problems (IBVP) for several fourth-order variations of the traditional diffusion equa…
Optimal control on a brain tumor growth model with lactate metabolism, viscoelastic effects, and tissue damage
Giulia Cavalleri, Alain Miranville
In this paper, we study an optimal control problem for a brain tumor growth model that incorporates lactate metabolism, viscoelastic effects, and tissue damage. The PDE system, int…
On a Brain Tumor Growth Model with Lactate Metabolism, Viscoelastic Effects, and Tissue Damage
Giulia Cavalleri, Pierluigi Colli, Alain Miranville +1
In this paper, we study a nonlinearly coupled initial-boundary value problem describing the evolution of brain tumor growth including lactate metabolism. In our modeling approach,…