On weak solutions of semilinear hyperbolic-parabolic equations.
One-dimensional model describing the non-linear viscoelastic response of materials
In this paper we consider a model of a one-dimensional body where strain depends on the history of stress. We show local existence for large data and global existence for small data of classical solutions and convergence of the displacement, strain and stress to zero for time going to infinity.
Paramétrix et propagation des singularités pour un problème de Cauchy à multiplicité variable
Perturbation index of linear partial differential-algebraic equations with a hyperbolic part
This paper deals with linear partial differential-algebraic equations (PDAEs) which have a hyperbolic part. If the spatial differential operator satisfies a Gårding-type inequality in a suitable function space setting, a perturbation index can be defined. Theoretical and practical examples are considered.
Problèmes mixtes pour des systèmes hyperboliques singuliers
Régularité de problèmes aux limites de type Hermite et Tricomi
Riemann-Hilbert problem and solvability of differential equations.
Schwache Lösungen des Frankl-Morawetz-Problems im ...3.
Smoothing effect and regularity for evolution integrodifferential systems
Solution of a transmission problem for semilinear parabolic-hyperbolic equations by the time-discretization method.
Solutions à près de systèmes d’équations aux dérivées partielles non linéaires de type mixte posés sur des ouverts non bornés
La résolution d’un système d’EDP non linéaires, de type mixte et sous contraintes, est étudiée dans des ouverts non bornés. Le cas considéré est celui d’un modèle d’écoulement transsonique avec condition d’entropie. Le problème est ramené à l’annulation d’une fonctionnelle positive pénalisée, dans un cadre hilbertien. Des solutions généralisées à près sont obtenues par encadrement de la borne inférieure de la fonctionnelle. Si les contraintes sont omises et sous certaines hypothèses, un algorithme...
Solutions of a nonhyperbolic pair of balance laws
We describe a constructive algorithm for obtaining smooth solutions of a nonlinear, nonhyperbolic pair of balance laws modeling incompressible two-phase flow in one space dimension and time. Solutions are found as stationary solutions of a related hyperbolic system, based on the introduction of an artificial time variable. As may be expected for such nonhyperbolic systems, in general the solutions obtained do not satisfy both components of the given initial data. This deficiency may be overcome,...
Solutions of a nonhyperbolic pair of balance laws
We describe a constructive algorithm for obtaining smooth solutions of a nonlinear, nonhyperbolic pair of balance laws modeling incompressible two-phase flow in one space dimension and time. Solutions are found as stationary solutions of a related hyperbolic system, based on the introduction of an artificial time variable. As may be expected for such nonhyperbolic systems, in general the solutions obtained do not satisfy both components of the given initial data. This deficiency may be overcome,...
Solutions of fourth-order partial differential equations in a noise removal model.
Solvability of a boundary-value problem for transonic flow in a nozzle.
Some nonclassical boundary value problems for linear mixed-type equations.
Some non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type
In this work two non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type are considered. Unique solvability of these problems is proven. The uniqueness of the solution is proven by the method of energy integrals and the existence is proven by the method of integral equations.
Spectral properties of a solution to the Gellerstedt problem for mixed-type equations and their applications.
Su un'equazione astratta di tipo Tricomi
Systems of reaction-diffusion equations with spatially distributed hysteresis
We study systems of reaction-diffusion equations with discontinuous spatially distributed hysteresis on the right-hand side. The input of the hysteresis is given by a vector-valued function of space and time. Such systems describe hysteretic interaction of non-diffusive (bacteria, cells, etc.) and diffusive (nutrient, proteins, etc.) substances leading to formation of spatial patterns. We provide sufficient conditions under which the problem is well posed in spite of the assumed discontinuity of...