Corrado Mascia

Travelling wave solutions for a balance law

We study entropy travelling wave solutions for first-order hyperbolic balance laws. Results concerning existence, regularity and asymptotic stability of such solutions are proved for convex fluxes and source terms with simple isolated zeros.

Metastability for nonlinear parabolic equations with application to scalar viscous conservation laws

The aim of this paper is to contribute to the definition of a versatile language for metastability in the context of partial differential equations of evolutive type. A general framework suited for parabolic equations in one-dimensional bounded domains is proposed, based on choosing a family of approximate steady states

Spectral stability of weak relaxation shock profiles

\{U^{\varepsilon}(\cdot;\xi) \}_{{}_{\xi \in J}}

STABILITY OF SCALAR RADIATIVE SHOCK PROFILES

and on the spectral properties of the linearized operators at such states. The slow motion for solutions belonging to a cylindrical neighborhood of the family

Continuity in finite time of entropy solutions for nonconvex conservation laws with reaction term

\{U^{\varepsilon}\}

Analytical and numerical investigation of traveling waves for the Allen–Cahn model with relaxation

is analyzed by means of a system of an ODE for the parameter

Nonlinear Hyperbolic–Elliptic Coupled Systems Arising in Radiation Dynamics

\xi=\xi(t)

Stability and Instability Issues for Relaxation Shock Profiles

, coupled with a PDE describing the evolution of the perturbation

Systems Biology Approach and Mathematical Modeling for Analyzing Phase-Space Switch During Epithelial-Mesenchymal Transition

v:=u-U^\varepsilon(\cdot;\xi)

L p – L q decay estimates for dissipative linear hyperbolic systems in 1D

. We state and prove a general result concerning the reduced system for the couple