Global classical solutions for partially dissipative hyperbolic system of balance laws

This work is concerned with ($N$-component) hyperbolic system of balance laws in arbitrary space dimensions. Under entropy dissipative assumption and the Shizuta-Kawashima algebraic condition, a general theory on the well-posedness of classical solutions in the framework of Chemin-Lerner's spaces with critical regularity is established. To do this, we first explore the functional space theory and develop an elementary fact that indicates the relation between homogeneous and inhomogeneous Chemin-Lerner's spaces. Then this fact allows to prove the local well-posedness for general data and global well-posedness for small data by using the Fourier frequency-localization argument. Finally, we apply the new existence theory to a specific fluid model-the compressible Euler equations with damping, and obtain the corresponding results in critical spaces.Comment: 39 page

A mathematical model for the SO_2 aggression to calcium carbonate stones: numerical approximation and asymptotic analysis

We introduce a degenerate nonlinear parabolic system which describes the chemical aggression of Calcium Carbonate stones under the attack of SO_2. For this system, we present some finite elements and finite differences schemes to approximate its solutions. Numerical stability is given under suitable CFL conditions. Finally, by means of a formal scaling, the qualitative behavior of the solutions for large times is investigated and a numerical verification of this asymptotics is given. Our results are in perfect agreement with the experimental behavior observed in the chemical literature

A MATHEMATICAL MODEL FOR THE SULPHUR DIOXIDE AGGRESSION TO CALCIUM CARBONATE STONES: NUMERICAL APPROXIMATION AND ASYMPTOTIC ANALYSIS ∗

Abstract. We introduce a degenerate nonlinear parabolic system that describes the chemical aggression of calcium carbonate stones under the attack of sulphur dioxide. For this system, we present some finite element and finite difference schemes to approximate its solutions. Numerical stability is given under suitable CFL conditions. Finally, by means of a formal scaling, the qualitative behavior of the solutions for large times is investigated, and a numerical verification of this asymptotics is given. Our results are in qualitative agreement with the experimental behavior observed in the chemical literature

Convergence of numerical algorithms for semilinear hyperbolic systems

Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

Convergence of relaxation schemes for conservation laws

Consiglio Nazionale delle Ricerche (CNR). Biblioteca Centrale / CNR - Consiglio Nazionale delle RichercheSIGLEITItal