A comparison theorem for nonlinear operators
A -Laplacian system with resonance and nonlinear boundary conditions on an unbounded domain
We study a nonlinear elliptic system with resonance part and nonlinear boundary conditions on an unbounded domain. Our approach is variational and is based on the well known Landesman-Laser type conditions.
A simple proof of the propagation of singularities for solutions of Hamilton-Jacobi equations
In Albano-Cannarsa [1] the authors proved that, under some conditions, the singularities of the semiconcave viscosity solutions of the Hamilton-Jacobi equation propagate along generalized characteristics. In this note we will provide a simple proof of this interesting result.
A viscosity solution method for Shape-From-Shading without image boundary data
In this paper we propose a solution of the Lambertian shape-from-shading (SFS) problem by designing a new mathematical framework based on the notion of viscosity solution. The power of our approach is twofolds: (1) it defines a notion of weak solutions (in the viscosity sense) which does not necessarily require boundary data. Moreover, it allows to characterize the viscosity solutions by their “minimums”; and (2) it unifies the works of [Rouy and Tourin, SIAM J. Numer. Anal.29 (1992) 867–884],...
A-Quasiconvexity: Relaxation and Homogenization
Integral representation of relaxed energies and of Γ-limits of functionals are obtained when sequences of fields v may develop oscillations and are constrained to satisfy a system of first order linear partial differential equations. This framework includes the treatement of divergence-free fields, Maxwell's equations in micromagnetics, and curl-free fields. In the latter case classical relaxation theorems in W1,p, are recovered.
Calculations of the hurricane eye motion based on singularity propagation theory.
Comparison of differential representations for radially symmetric Stokes flow.
Concerning some version of the Lax-Milgram Lemma in normed spaces
Continuity of solutions of linear, degenerate elliptic equations
We consider the simplest form of a second order, linear, degenerate, elliptic equation with divergence structure in the plane. Under an integrability condition on the degenerate function, we prove that the solutions are continuous.
Equivalent formulations of generalized von Kármán equations for circular viscoelastic plates
The paper deals with the analysis of generalized von Kármán equations which desribe stability of a thin circular viscoelastic clamped plate of constant thickness under a uniform compressible load which is applied along its edge and depends on a real parameter. The meaning of a solution of the mathematical problem is extended and various equivalent reformulations of the problem are considered. The structural pattern of the generalized von Kármán equations is analyzed from the point of view of nonlinear...
Exact solution of the time fractional variant Boussinesq-Burgers equations
In the present article, we consider a nonlinear time fractional system of variant Boussinesq-Burgers equations. Using Lie group analysis, we derive the infinitesimal groups of transformations containing some arbitrary constants. Next, we obtain the system of optimal algebras for the symmetry group of transformations. Afterward, we consider one of the optimal algebras and construct similarity variables, which reduces the given system of fractional partial differential equations (FPDEs) to fractional...
Existence and uniqueness of generalized solutions to a telegraph equation with an integral boundary condition via Galerkin's method.
Faisceaux constructibles et systèmes holonomes d'équations aux dérivées partielles linéaires à points singuliers réguliers
Iterati di operatori e regolarità Gevrey microlocale anisotropa
Laplace transform of distribution-valued functions and its applications
On a generalized nonlinear equation of Schrödinger type.
On a nonlocal problem for a confined plasma in a Tokamak
The paper deals with a nonlocal problem related to the equilibrium of a confined plasma in a Tokamak machine. This problem involves terms and , which are neither local, nor continuous, nor monotone. By using the Galerkin approximate method and establishing some properties of the decreasing rearrangement, we prove the existence of solutions to such problem.
On global solutions to a nonlinear Alfvén wave equation
We establish the global existence and uniqueness of smooth solutions to a nonlinear Alfvén wave equation arising in a finite-beta plasma. In addition, the spatial asymptotic behavior of the solution is discussed.
On optimal decay rates for weak solutions to the Navier-Stokes equations in
This paper is concerned with optimal lower bounds of decay rates for solutions to the Navier-Stokes equations in . Necessary and sufficient conditions are given such that the corresponding Navier-Stokes solutions are shown to satisfy the algebraic bound
On the convolution equations over the quarter-plane.