Asymptotic behavior for numerical solutions of a semilinear parabolic equation with a nonlinear boundary condition.
Asymptotic Behavior of Fundamental Solutions and Potential Theory of Prabolic Operators with Variable Coeeficients.
Asymptotic behaviour of the weighted trace of the Schrödinger operator.
Asymptotic solutions to Fuchsian equations in several variables
The aim of this paper is to construct asymptotic solutions to multidimensional Fuchsian equations near points of their degeneracy. Such construction is based on the theory of resurgent functions of several complex variables worked out by the authors in [1]. This theory allows us to construct explicit resurgent solutions to Fuchsian equations and also to investigate evolution equations (Cauchy problems) with operators of Fuchsian type in their right-hand parts.
Asymptotics for some Green Kernels on the Heisenberg Group and the Martin Boundary.
Asymptotique des pôles de la matrice de scattering pour deux obstacles strictement convexes
Asymptotique des résonances pour des obstacles
Bäcklund-Darboux transformation for non-isospectral canonical system and Riemann-Hilbert problem.
Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type
We establish the existence, uniqueness and main properties of the fundamental solutions for the fractional porous medium equation introduced in [51]. They are self-similar functions of the form with suitable and . As a main application of this construction, we prove that the asymptotic behaviour of general solutions is represented by such special solutions. Very singular solutions are also constructed. Among other interesting qualitative properties of the equation we prove an Aleksandrov reflection...
Behaviour of symmetric solutions of a nonlinear elliptic field equation in the semi-classical limit: Concentration around a circle.
Benjamin-Ono equation on a half-line.
Besov algebras on Lie groups of polynomial growth
We prove an algebra property under pointwise multiplication for Besov spaces defined on Lie groups of polynomial growth. When the setting is restricted to H-type groups, this algebra property is generalized to paraproduct estimates.
Bestimmung und Anwendung von Vekua-Resolventen.
Bifurcation analysis of macroscopic traffic flow model based on the influence of road conditions
A macroscopic traffic flow model considering the effects of curves, ramps, and adverse weather is proposed, and nonlinear bifurcation theory is used to describe and predict nonlinear traffic phenomena on highways from the perspective of global stability of the traffic system. Firstly, the stability conditions of the model shock wave were investigated using the linear stability analysis method. Then, the long-wave mode at the coarse-grained scale is considered, and the model is analyzed using the...
Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents
Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues
We prove existence and bifurcation results for a semilinear eigenvalue problem in , where the linearization — has no eigenvalues. In particular, we show...
Biting theorems for jacobians and their applications
Blow up for the critical gKdV equation. II: Minimal mass dynamics
We consider the mass critical (gKdV) equation for initial data in . We first prove the existence and uniqueness in the energy space of a minimal mass blow up solution and give a sharp description of the corresponding blow up soliton-like bubble. We then show that this solution is the universal attractor of all solutions near the ground state which have a defocusing behavior. This allows us to sharpen the description of near soliton dynamics obtained in [29].
Blow-up for solutions of hyperbolic PDE and spacetime singularities
An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime singularities is naturally related to blow-up phenomena for nonlinear hyperbolic systems. These connections are explained and recent progress in applying the theory of hyperbolic equations in this field is presented. A direction which has turned out to be fruitful is that...
Blow-up for the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential
We give a sufficient condition under which the solutions of the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential blow up. The method is a modified variational approach, in the spirit of the work by Ibrahim et al. [Anal. PDE 4 (2011), 405-460].