Generalized Solutions to Cauchy Problems.
Gevrey solvability for semilinear partial differential equations with multiple characteristics
Vengono considerate equazioni alle derivate parziali semilineari con caratteristiche multiple. Si studia in particolare la loro risolubilità locale e la buona positura del problema di Cauchy nell'ambito delle classi di Gevrey.
Global asymptotic stability of solutions to nonlinear marine riser equation.
Global existence and asymptotic behavior of solutions for the Klein-Gordon equations with quadratic nonlinearity in two space dimensions.
Global well-posedness of the Cauchy problem of a higher-order Schrödinger equation.
Incompressible limit of a fluid-particle interaction model
The incompressible limit of the weak solutions to a fluid-particle interaction model is studied in this paper. By using the relative entropy method and refined energy analysis, we show that, for well-prepared initial data, the weak solutions of the compressible fluid-particle interaction model converge to the strong solution of the incompressible Navier-Stokes equations as long as the Mach number goes to zero. Furthermore, the desired convergence rates are also obtained.
Initial boundary value problems of the Degasperis-Procesi equation
We mainly study initial boundary value problems for the Degasperis-Procesi equation on the half line and on a compact interval. By the symmetry of the equation, we can convert these boundary value problems into Cauchy problems on the line and on the circle, respectively. Applying thus known results for the equation on the line and on the circle, we first obtain the local well-posedness of the initial boundary value problems. Then we present some blow-up and global existence results for strong solutions....
Integrable hierarchy of higher nonlinear Schrödinger type equations.
Interaction des singularités pour les équations de Klein-Gordon non linéaires
Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d'espace
Local and global nonexistence of solutions to semilinear evolution equations.
Local Well-Posedness for Higher Order Nonlinear Dispersive Systems.
Local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation in Besov spaces
We study local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation for the initial data u₀(x) in the Besov space with max(3/2,1 + 1/p) < s ≤ m and (p,r) ∈ [1,∞]², where g:ℝ → ℝ is a given -function (m ≥ 4) with g(0)=g’(0)=0, and κ ≥ 0 and γ ∈ ℝ are fixed constants. Using estimates for the transport equation in the framework of Besov spaces, compactness arguments and Littlewood-Paley theory, we get a local well-posedness result.
New method of solving the system of differential partial equations of any number of equations, of any number of functions and of any order
Non linear evolution equations Cauchy problem and scattering theory
Nonexistence of minimal blow-up solutions of equations in
Nonexistence of solutions to systems of higher-order semilinear inequalities in cone-like domains.
Nonlinear evolution inclusions arising from phase change models
The paper is devoted to the analysis of an abstract evolution inclusion with a non-invertible operator, motivated by problems arising in nonlocal phase separation modeling. Existence, uniqueness, and long-time behaviour of the solution to the related Cauchy problem are discussed in detail.
Nonlinear evolution PDEs in : existence and uniqueness of solutions, asymptotic and Borel summability properties
On a Class of non Linear Schrödinger Equations with non Local Interaction.