Existence and uniqueness of solutions of quasilinear hyperbolic systems of partial differential-functional equations
Existence of critical sub-solutions of the Hamilton–Jacobi equation on compact manifolds
Existence, uniqueness and continuous dependence for a hereditary nonlinear functional partial differential equation of the first order
Existence, uniqueness and stability for spatially inhomogeneous Becker-Döring equations with diffusion and convection terms
We consider the spatially inhomogeneous Bekker-Döring infinite-dimensional kinetic system describing the evolution of coagulating and fragmenting particles under the influence of convection and diffusion. The simultaneous consideration of opposite coagulating and fragmenting processes causes many additional difficulties in the investigation of spatially inhomogeneous problems, where the space variable changes differently for distinct particle sizes. To overcome these difficulties, we use a modified...
Explicit definition of an exact measure for the semiflow of a first order partial differential equation
Formation of singularities for viscosity solutions of Hamilton-Jacobi equations
Frentes de explosión en ecuaciones de Hamilton Jacobi por argumentos de control determinista.
Generalized Cauchy problems for hyperbolic functional differential systems
A generalized Cauchy problem for hyperbolic functional differential systems is considered. The initial problem is transformed into a system of functional integral equations. The existence of solutions of this system is proved by using the method of successive approximations. Differentiability of solutions with respect to initial functions is proved. It is important that functional differential systems considered in this paper do not satisfy the Volterra condition.
Generalized Solutions to Nonlinear First-Order Systems.
Global smooth solutions of some quasi-linear hyperbolic systems with large data
Hamilton-Jacobi flows and characterization of solutions of Aronsson equations
In this note, we verify the conjecture of Barron, Evans and Jensen [3] regarding the characterization of viscosity solutions of general Aronsson equations in terms of the properties of associated forward and backwards Hamilton-Jacobi flows. A special case of this result is analogous to the characterization of infinity harmonic functions in terms of convexity and concavity of the functions and , respectively.
Hopf-type estimates for solutions to Hamilton-Jacobi equations with concave-convex initial data.
Implicit difference methods for nonlinear first order partial functional differential systems
Initial problems for nonlinear hyperbolic functional differential systems are considered. Classical solutions are approximated by solutions of suitable quasilinear systems of difference functional equations. The numerical methods used are difference schemes which are implicit with respect to the time variable. Theorems on convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability is based on a comparison technique with nonlinear estimates...
Mathematical and numerical analysis of an alternative well-posed two-layer turbulence model
In this article, we wish to investigate the behavior of a two-layer turbulence model from the mathematical point of view, as this model is useful for the near-wall treatment in numerical simulations. First, we explain the difficulties inherent in the model. Then, we present a new variable that enables the mathematical study. Due to a problem of definition of the turbulent viscosity on the wall boundary, we consider an alternative version of the original equation. We show that some physical aspects...
Mathematical and Numerical Analysis of an Alternative Well-Posed Two-Layer Turbulence Model
In this article, we wish to investigate the behavior of a two-layer k - ε turbulence model from the mathematical point of view, as this model is useful for the near-wall treatment in numerical simulations. First, we explain the difficulties inherent in the model. Then, we present a new variable θ that enables the mathematical study. Due to a problem of definition of the turbulent viscosity on the wall boundary, we consider an alternative version of the original equation. We show that some physical...
New Approach to Shocks Generation for Conservation Laws. Example: Global Solution to Hopf Equation
Non unicité de Hölmgren pour des problèmes non linéaires
Nonlinear multidimensional parabolic-hyperbolic equations.
On Bressan's conjecture on mixing properties of vector fields
In [9], the author considers a sequence of invertible maps which exchange the positions of adjacent intervals on the unit circle, and defines as Aₙ the image of the set 0 ≤ x ≤ 1/2 under the action of Tₙ ∘ ... ∘ T₁, (1) Aₙ = (Tₙ ∘ ... ∘ T₁)x₁ ≤ 1/2. Then, if Aₙ is mixed up to scale h, it is proved that (2) . We prove that (1) holds for general quasi incompressible invertible BV maps on ℝ, and that this estimate implies that the map Tₙ ∘ ... ∘ T₁ belongs to the Besov space , and its norm is bounded...
On global solutions for the Vlasov-Poisson system.