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In this paper, we first derive the compressible Navier-Stokes/Landau-Lifshitz-Gilbert (NS-LLG) model for magnetoelastic materials via the energetic variational approach (EnVarA). It is important to emphasize that the manner in which the…
We introduce a new family of p-adic non-linear evolution equations. We establish the local well-posedness of the Cauchy problem for these equations in Sobolev-type spaces. For a certain subfamily, we show that the blow-up phenomenon occurs…
We study the three-dimensional cubic nonlinear wave equation (NLW) with random initial data below $L^2(\mathbb{T}^3)$. By considering the second order expansion in terms of the random linear solution, we prove almost sure local…
This paper is concerned with the strong solution to the Cauchy-Dirichlet problem for backward stochastic partial differential equations of parabolic type. Existence and uniqueness theorems are obtained, due to an application of the…
We consider the time-dependent Landau-Lifshitz-Gilbert equation. We prove that each weak solution coincides with the (unique) strong solution, as long as the latter exists in time. Unlike available results in the literature, our analysis…
The dynamics of magnetization near a stable equilibrium in ferromagnetic nanomagnets are examined within the Landau--Lifshitz--Gilbert (LLG) framework. For a small angle precession, the dependence of ferromagnetic resonance (FMR) frequency,…
Given a positive energy solution of the Klein-Gordon equation, the motion of the free, spinless, relativistic particle is described in a fixed Lorentz frame by a Markov diffusion process with non-constant diffusion coefficient. Proper time…
This paper establishes the global well-posedness of the Landau-Lifshitz-Baryakhtar (LLBar) equation in the whole space $\mathbb{R}^3$. The study first demonstrates the existence and uniqueness of global strong solutions using the weak…
The Landau--Lifshitz--Bloch (LLB) equation is a well-established micromagnetic model for describing magnetisation dynamics in ferromagnets at elevated temperatures. In this paper, we propose and analyse two fully discrete, conforming finite…
Nonlinear localized magnetic excitations in one dimensional magnonic crystal is investigated under periodic magntic field. The governing Landau-Lifshitz equation is transformed into variable coefficient nonlinear Schrodinger equation(VCNLS)…
The blow-up phenomena of stochastic semilinear parabolic equations with additive as well as linear multiplicative L\'evy noises are investigated in this work. By suitably modifying the concavity method in the stochastic context, we…
In this paper, complex Ginzburg-Landau (CGL) equations with superlinear growth terms are studied. We discuss the local well-posedness in the energy space H1 for the initial-boundary value problem of the equations in general domains. The…
We consider the nonlinear Schr\"odinger equation on the $d$-dimensional torus $\mathbb T^d$, with the nonlinearity of polynomial type $|u|^{2\sigma}u$. For any $\sigma \in \mathbb N$ and $s>\frac d2$ we prove that adding to this equation a…
In this paper we consider a stochastic Keller-Segel type equation, perturbed with random noise. We establish that for special types of random pertubations (i.e. in a divergence form), the equation has a global weak solution for small…
We prove the existence of time periodic solution to the 3D Ginzburg-Landau equation in weighted Sobolev spaces. We consider the cubic Ginzburg-Landau equation with an external force $g$ satisfying the oddness condition $g(-x,t)=-g(x,t)$.…
We introduce a generalized Gross-Pitaevskii equation that provides a nonlinear framework for studying two-dimensional (2D) attractive Bose systems. Its defining feature is the logarithmic density dependence of the coupling constant, which…
This paper would focus on the subject of the 2-D incompressible Navier-Stokes-Cahn-Hilliard (NS-CH) system with a singular free energy density. Due to lack of the maximum principle for the convective Cahn-Hilliard equation (as a…
We study the logarithmic Schr\"odinger equation with finite range potential on $\mathbb{R}^{\mathbb{Z}^d}$. Through a ground-state representation, we associate and construct a global Gibbs measure and show that it satisfies a logarithmic…
We study linear pseudoparabolic equations with unbounded and time-dependent coefficients. We solve the case which has remained open in several recent studies of pseudoparabolic equations with unbounded and time-dependent coefficients. In…
We revisit the work [L. Campos and J. Murphy, SIAM J. Math. Anal., 55 (2023), pp. 3807--3843], which classified the dynamics of $H^1$ solutions at the ground state threshold for cubic inhomogeneous nonlinear Schr\"odinger equations of the…