Solutions analytiques de l'équation d'Euler d'un fluide compressible
Solvability for semilinear PDE with multiple characteristics
We prove local solvability in Gevrey spaces for a class of semilinear partial differential equations. The linear part admits characteristics of multiplicity k ≥ 2 and data are fixed in , 1 < σ < k/(k-1). The nonlinearity, containing derivatives of lower order, is assumed of class with respect to all variables.
Solvable nonlinear evolution PDEs in multidimensional space.
Some nonexistence results for higher-order evolution inequalities in cone-like domains.
Temperature-dependent hysteresis in one-dimensional thermovisco-elastoplasticity
In this paper, we develop a thermodynamically consistent description of the uniaxial behavior of thermovisco-elastoplastic materials for which the total stress contains, in addition to elastic, viscous and thermic contributions, a plastic component of the form . Here and are the fields of strain and absolute temperature, respectively, and denotes a family of (rate-independent) hysteresis operators of Prandtl-Ishlinskii type, parametrized by the absolute temperature. The system of momentum...
The Cauchy problem for the coupled Klein-Gordon-Schrödinger system
We consider the Cauchy problem for a generalized Klein-Gordon-Schrödinger system with Yukawa coupling. We prove the existence of global weak solutions by the compactness method and, through a special choice of the admissible pairs to match two types of equations, we prove the uniqueness of those solutions by an approach similar to the method presented by J. Ginibre and G. Velo for the pure Klein-Gordon equation or pure Schrödinger equation. Though it is very simple in form, the method has an unnatural...
The geometry of the space of Cauchy data of nonlinear PDEs
First-order jet bundles can be put at the foundations of the modern geometric approach to nonlinear PDEs, since higher-order jet bundles can be seen as constrained iterated jet bundles. The definition of first-order jet bundles can be given in many equivalent ways - for instance, by means of Grassmann bundles. In this paper we generalize it by means of flag bundles, and develop the corresponding theory for higher-oder and infinite-order jet bundles. We show that this is a natural geometric framework...
The homogeneous balance of undetermined coefficients method and its application
The homogeneous balance of undetermined coefficients method is firstly proposed to solve such nonlinear partial differential equations (PDEs), the balance numbers of which are not positive integers. The proposed method can also be used to derive more general bilinear equation of nonlinear PDEs. The Eckhaus equation, the KdV equation and the generalized Boussinesq equation are chosen to illustrate the validity of our method. The proposed method is also a standard and computable method, which can...
The Semilinear Second-Order Hyperbolic Equation with Data Strongly Singular at One Point.
Uniform local null control of the Leray-α model
This paper deals with the distributed and boundary controllability of the so called Leray-α model. This is a regularized variant of the Navier−Stokes system (α is a small positive parameter) that can also be viewed as a model for turbulent flows. We prove that the Leray-α equations are locally null controllable, with controls bounded independently of α. We also prove that, if the initial data are sufficiently small, the controls converge as α → 0+ to a null control of the Navier−Stokes equations....
Viscosity solutions of the Cauchy problem for second-order nonlinear partial differential equations in Hilbert spaces.
Well-posed solutions of the third order Benjamin-Ono equation in weighted Sobolev spaces.
Well-posedness and regularity for a parabolic-hyperbolic Penrose-Fife phase field system
This work is concerned with the study of an initial boundary value problem for a non-conserved phase field system arising from the Penrose-Fife approach to the kinetics of phase transitions. The system couples a nonlinear parabolic equation for the absolute temperature with a nonlinear hyperbolic equation for the phase variable , which is characterized by the presence of an inertial term multiplied by a small positive coefficient . This feature is the main consequence of supposing that the response...
Well-posedness for some perturbations of the KdV equation with low regularity data.
Young-measure approximations for elastodynamics with non-monotone stress-strain relations
Microstructures in phase-transitions of alloys are modeled by the energy minimization of a nonconvex energy density . Their time-evolution leads to a nonlinear wave equation with the non-monotone stress-strain relation plus proper boundary and initial conditions. This hyperbolic-elliptic initial-boundary value problem of changing types allows, in general, solely Young-measure solutions. This paper introduces a fully-numerical time-space discretization of this equation in a corresponding very...
Young-Measure approximations for elastodynamics with non-monotone stress-strain relations
Microstructures in phase-transitions of alloys are modeled by the energy minimization of a nonconvex energy density ϕ. Their time-evolution leads to a nonlinear wave equation with the non-monotone stress-strain relation plus proper boundary and initial conditions. This hyperbolic-elliptic initial-boundary value problem of changing types allows, in general, solely Young-measure solutions. This paper introduces a fully-numerical time-space discretization of this equation in a corresponding...
Асимптотика решения задачи Коши для уравнения Кортевега-де Фриза с начальными данными типа ступеньки
Длинноволновая асимптотика решения нелинейной системы уравнений с малой диссипацией.
Изометрические погружения областей n-мерного пространства Лобачевского в евклидовы пространства с плоской нормальной связностью. Модель калибровочного поля
О решении задачи Коши для уравнения Кортевега-де Фриза с начальными данными, являющимися суммой периодической и быстроубывающей функции