Related papers: Existence of solutions for a mathematical model re…
In this work, we analytically investigate a degenerating PDE system for phase separation and complete damage processes considered on a nonsmooth time-dependent domain with mixed boundary conditions. The evolution of the system is described…
Lattice dynamical methods used to predict phase-transformations in crystals typically evaluate the harmonic phonon spectra and therefore do not work in frequent and important situations where the crystal structure is unstable in the…
The problem of heterogeneous nucleation of second-phase in alloys in the vicinity of elastic defects is considered. The defect can be a dislocation line or a crack tip residing in a crystalline solid. We use the Ginzburg-Landau equation to…
In this paper, we present a framework for Stability Analysis of Systems of Coupled Linear Partial-Differential Equations. The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichelet,…
The two-dimensional generalization of the Polyelectolite model of DNA is proposed. It is reduced to the boundary problem for nonlinear completely integrable equation $\sh$-Gordon. In the linearisible version the exact solution is…
We analyze the thermodynamics of the focusing discrete nonlinear Schr\"odinger equation in dimensions $d\ge 3$ with general nonlinearity $p>1$ and under a model with two parameters, representing inverse temperature and strength of the…
We establish the long-time existence of large-data weak solutions to a system of nonlinear partial differential equations. The system of interest governs the motion of non-Newtonian fluids described by a simplified viscoelastic rate-type…
Despite the fundamental importance of solid--solid transitions for metallurgy, ceramics, earth science, reconfigurable materials, and colloidal matter, the details of how materials transform between two solid structures are poorly…
We resolve issues that have plagued reliable prediction of relative phase stability for solid-solutions and compounds. Due to its commercially important phase diagram, we showcase Al-Li system because historically density-functional theory…
This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations (SPDEs) with multiplicative noise. The nonlinearity in the diffusion term of the SPDEs is assumed to…
We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…
We prove the well-posedness results, i.e. existence, uniqueness, and stability, of the solutions to a class of nonlocal fully nonlinear parabolic partial differential equations (PDEs), where there is an external time parameter $t$ on top of…
Phase-change materials based on Ge-Sb-Te alloys are widely used in industrial applications such as nonvolatile memories, but reaction pathways for crystalline-to-amorphous phase-change on picosecond timescales remain unknown. Femtosecond…
We present a computer simulation study of the crystalline phases of hard ellipsoids of revolution. A previous study [Phys. Rev. E, \textbf{75}, 020402 (2007)] showed that for aspect ratios $a/b\ge 3$ the previously suggested stretched-fcc…
In this paper we prove existence of global in time weak solutions for a highly nonlinear PDE system arising in the context of damage phenomena in thermoviscoelastic materials. The main novelty of the present contribution with respect to the…
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…
We study fully nonlinear second-order (forward) stochastic partial differential equations (SPDEs). They can also be viewed as forward path-dependent PDEs (PPDEs) and will be treated as rough PDEs (RPDEs) under a unified framework. We…
This paper presents a safe stabilization of the Stefan PDE model with a moving boundary governed by a high-order dynamics. We consider a parabolic PDE with a time-varying domain governed by a second-order response with respect to the…
We study the well-posedness and asymptotic behaviour of selected PDE-PDE and PDE-ODE systems on one-dimensional spatial domains, namely a boundary coupled wave-heat system and a wave equation with a dynamic boundary condition. We prove…