Related papers: A dual variational principle for nonlinear disloca…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
We derive the dual variational principle (principle of minimal complementary energy) for the nonlocal nonlinear scalar diffusion problem, which may be viewed as the nonlocal version of the $p$-Laplacian operator. We establish existence and…
Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for…
The pre-image topological pressure is defined for bundle random dynamical systems. A variational principle for it has also been given.
An existence result is proved for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions.…
It has been shown in experiments that self-climb of prismatic dislocation loops by pipe diffusion plays important roles in their dynamical behaviors, e.g., coarsening of prismatic loops upon annealing, as well as the physical and mechanical…
We present a dynamical theory of a two-dimensional martensitic transition in an elastic solid, connecting a high-temperature phase which is nondegenerate and has triangular symmetry, and a low-temperature phase which is triply degenerate…
This paper focuses on an elastic dislocation problem that is motivated by applications in the geophysical and seismological communities. In our model, the displacement satisfies the Lam\'e system in a bounded domain with a mixed homogeneous…
Similar evolutionary variational inequalities appear as convenient formulations for continuous quasistationary models for sandpile growth, formation of a network of lakes and rivers, magnetization of type-II superconductors, and…
Variational formulations of statics and dynamics of mechanical systems controlled by external forces are presented as examples of variational principles.
This work presents a generalized physical interpretation of unconventional dispersion asymmetries associated moving elastic solids. By shifting the notion from systems with time-variant material fields to physically traveling materials, the…
We study nonlinear dispersive wave systems described by hyperbolic PDE's in R^{d} and difference equations on the lattice Z^{d}. The systems involve two small parameters: one is the ratio of the slow and the fast time scales, and another…
In this work, we introduce a degenerating PDE system with a time-depending domain for complete damage processes under time-varying Dirichlet boundary conditions. The evolution of the system is described by a doubly nonlinear differential…
We consider an isotropic compressible non-dissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk dynamics of the fluid as well as the free…
A partial differential equation model is analyzed for the two-slit experiment of quantum mechanics. The state variable of the equation is the probability density function of particle positions. The equation has a diffusion term…
In this article we study a system of nonlinear PDEs modelling the electrokinetics of a nematic electrolyte material consisting of various ions species contained in a nematic liquid crystal. The evolution is described by a system coupling a…
The thermodynamic theory of dislocation-enabled plasticity is based on two unconventional hypotheses. The first of these is that a system of dislocations, driven by external forces and irreversibly exchanging heat with its environment, must…
In order to identify the exact criteria for the formation of two-ring structures in galaxies, we studied the issue of gravitational instability of the corresponding structural vibration modes against the background of a composite disk model…
Using the principle of structural analogy of solutions, approaches have been developed for constructing exact solutions of complex nonlinear PDEs, including PDEs with delay, based on the use of special solutions to auxiliary simpler related…
This paper presents causal block-diagram models to represent the equations of motion of multi-body systems in a very compact and simple closed form. Both the forward dynamics (from the forces and torques imposed at the various…