相关论文: Periodic solutions to Kobayashi--Warren--Carter sy…

In this paper, the global qualitative analysis of planar quadratic dynamical systems is established and a new geometric approach to solving Hilbert's Sixteenth Problem in this special case of polynomial systems is suggested. Using geometric…

We construct fundamental solutions of second-order parabolic systems of divergence form with bounded and measurable leading coefficients and divergence free first-order coefficients in the class of $BMO^{-1}_x$, under the assumption that…

A multidimensional version of the Yamada-Watanabe theorem is proved. It implies a spectral matrix Yamada-Watanabe theorem. It is also applied to particle systems of squared Bessel processes, corresponding to matrix analogues of squared…

This paper is devoted to existence and non-existence results for generalized tran-sition waves solutions of space-time heterogeneous Fisher-KPP equations. When the coefficients of the equation are periodic in space but otherwise depend in a…

We prove an existence and uniqueness result for Neumann boundary problem of a parabolic partial differential equation (PDE for short) with a singular nonlinear divergence term which can only be understood in a weak sense. A probabilistic…

We propose a novel and systematic method for coarse-graining oscillator networks described by phase equations. Our coarse-graining method enables us to obtain the closed coarse-grained equations for a few effective eigenmodes, which is…

In this paper, we would establish the existence and stability of periodic solutions to the Benjamin-Bona-Mahony-Burgers (BBM-Burgers) equation in $H^1_0([0, 1])$, whose medium interior is applied with time-periodic force $f(x, t)$ with…

We formulate an effective-description framework for the dynamics of open quantum systems by extending the time-coarse-graining formalism to open systems. Our coarse-graining procedure efficiently removes high-frequency processes which are…

Two different aspects of parabolic iteration in the complex upper half-plane are considered here. First, from a noncommutative probability perspective, a Berry-Esseen type estimate for the convergence speed of the monotone central limit…

We present an existence and localization result for periodic solutions of second-order non-linear coupled planar systems, without requiring periodicity for the non-linearities. The arguments for the existence tool are based on a variation…

In this paper we propose local and global existence results for the solution of systems characterized by the coupling of ODEs and PDEs. The coexistence of distinct mathematical formalisms represents the main feature of hybrid approaches, in…

Motionless domains walls representing heteroclinic temporal or spatial orbits typically exist only for very specific parameters. This report introduces a novel mechanism for stabilizing temporal domain walls away from the Maxwell point…

This paper is devoted to the study of a nonlinear coupled system of two Korteweg-de Vries equations in a periodic domain under the effect of an internal damping term. The system was introduced Gear and Grimshaw to model the interactions of…

We are concerned with the study of the system of coupled equations of motion for a system of two-level atoms interacting with a single-mode field in the laser cavity on resonance. The passage from the equation of motion to the Lorenz…

We propose a nonlinear forward Feynman-Kac type equation, which represents the solution of a non-conservative semilinear parabolic Partial Differential Equations (PDE). We show in particular existence and uniqueness. The solution of that…

The main objective of this article are two-fold. First, we introduce some general principles on phase transition dynamics, including a new dynamic transition classification scheme, and a Ginzburg-Landau theory for modeling equilibrium phase…

We propose a framework to define solutions of ODE systems under a novel condition that goes well beyond the usual continuity condition required in the classical theory of ODEs (Peano's or Picard's theorems). We illustrate our results with…

We consider the conformal wave equation on the Einstein cylinder with a defocusing cubic non-linearity. Motivated by a method developed by Rostworowski-Maliborski on the existence of time periodic solutions to the spherically symmetric…

We study periodic solutions of a one-degree of freedom micro-electro-mechanical system (MEMS) with a parallel-plate capacitor under $T$--periodic electrostatic forcing. We obtain analytical results concerning the existence of $T-$ periodic…

This note presents a regularity result with proof for an initial-boundary value problem of a linear parabolic system involving curl of the unknown vector field, subjected to the boundary condition of prescribing the tangential component of…