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

This work is concerned with the identification problem for what we call the perturbation term or error term in a parabolic partial differential equation, through its approximate periodic solutions. The observation is made over a subregion…

Time-periodic weak solutions for a coupled hyperbolic-parabolic system are obtained. A linear heat and wave equation are considered on two respective $d$-dimensional spatial domains that share a common $(d-1)$-dimensional interface…

We study the homogenization property of systems of quasi-linear PDEs of parabolic type with periodic coefficients, highly oscillating drift and highly oscillating nonlinear term. To this end, we propose a probabilistic approach based on the…

Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…

In this article, basing upon probabilistic methods, we discuss periodic homogenization of a class of weakly coupled systems of linear elliptic and parabolic partial differential equations. Under the assumption that the systems have rapidly…

In this paper, we develop a new method to find the exact solutions of the Einstein's field equations by using which we construct time-periodic solutions. The singularities of the time-periodic solutions are investigated and some new…

We construct and study a fundamental solution of Cauchy's problem for p-adic parabolic equations of a certain the type. The fundamental solution is the transition density of a p-adic Markov process.

In this paper we provide conditions to ensure the existence, for $e>0$ sufficiently small, of periodic solutions of given period $T>0$ in a prescribed domain $U$ for a class of singularly perturbed first order differential systems. Here…

The paper deals with the initial value problem for linear systems of FDEs with variable coefficients involving Riemann--Liouville and Caputo derivatives. The technique of the generalized Peano--Baker series is used to obtain the…

In this paper, we consider a system of one-dimensional parabolic PDEs, known as the KWC system, as a phase-field model for grain boundary motion. A key feature of this system is that the equation for the crystalline orientation angle is…

We prove well-posedness results for the solution to an initial and boundary-value problem for an Allen-Cahn type equation describing the phenomenon of phase transitions for a material contained in a bounded and regular domain. The dynamic…

Time-periodic solutions to partial differential equations of parabolic type corresponding to an operator that is elliptic in the sense of Agmon-Douglis-Nirenberg are investigated. In the whole- and half-space case we construct an explicit…

This work is devoted to present Massera-type theorems for the Kawahara system, a higher order dispersive equation, posed in a bounded domain. Precisely, thanks to some properties of the semigroup and the decays of the solutions of this…

We present the Euler--Langrage equations for a many-body system of coupled planar pendulums. Hence, imposing initial condition data, the equations of motion are linearized and later developed in an idealized model for the pseudo-periodicity…

We propose to combine the Carleman estimate and the Newton method to solve an inverse source problem for nonlinear parabolic equations from lateral boundary data. The stability of this inverse source problem is conditionally logarithmic.…

In this paper, we are concerned with complex Ginzburg-Landau (CGL) equations. There are several results on the global existence and smoothing effects of solutions to the initial boundary value problem for (CGL) in bounded or unbounded…

We consider a state-of-the-art ferroelectric phase-field model arising from the engineering area in recent years, which is mathematically formulated as a coupled elliptic-parabolic differential system. We utilize a fixed point theorem based…

We prove existence and Sobolev regularity of solutions of a nonlinear system of degenerate-parabolic PDEs with self- and cross-diffusion, transport/confinement and nonlocal interaction terms. The macroscopic system of PDEs is formally…

We present a hybrid quantum-classical framework for solving general time-dependent parabolic partial differential equations (PDEs) using quantum variational circuits. Building on the QPINN approach, this method applies broadly to parabolic…

This paper deals with the Vlasov-Stokes' system in three dimensions with periodic boundary conditions in the spatial variable. We prove the existence of a unique strong solution to this two-phase model under the assumption that initial…