From the 1 of 7 linked papers with an AI index.
7 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…
Integral Representations for Interface Problems for the Barenblatt-Sobolev-Galpern Pseudoparabolic Equation
Andreas Chatziafratis, Sergey A. Rukolaine, Elias C. Aifantis
The paper derives new contour integral formulas using the Unified Transform Method to solve initial‑boundary‑value and interface problems for the Barenblatt‑Sobolev‑Galpern pseudo‑…
Rigorous analysis for the Dirac system on the quarter-plane
Hassan Babaei, Jerry L. Bona, Andreas Chatziafratis
Considered and analyzed below are fully non-homogeneous initial-boundary-value problems for the celebrated Dirac system, formulated on the spatial half-line. Analytical solution fo…
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…
Fokas-type closed-form solution formulae for Sobolev-type equations with time-dependent coefficients
Andreas Chatziafratis
We analytically derive novel explicit integral representations for the solution of nonhomogeneous initial-boundary-value problems for a large category of evolution partial differen…
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…