Related papers: Global bifurcation of anti-plane shear fronts
In this paper, we prove the global existence of strong solutions for the 3D incompressible inhomogeneous viscoelastic system. We do not assume the "initial state" assumption and the "div-curl" structure inspired by the works [59,61]. It is…
Crack-like objects that propagate along frictional interfaces, i.e.~frictional shear cracks, play a major role in a broad range of frictional phenomena. Such frictional cracks are commonly assumed to feature the universal square root…
A boundary value problem on an unbounded domain, associated to difference equations with the Euclidean mean curvature operator is considered. The existence of solutions which are positive on the whole domain and decaying at infinity is…
At the microscopic level, plastic flow of a jammed, disordered material consists of a series of particle rearrangements that cannot be reversed by subsequent deformation. An infinitesimal deformation of the same material has no…
We consider the cylindrical bending problem for an infinite plate as modelled with a family of generalized continuum models, including the micromorphic approach. The models allow to describe length scale effects in the sense that thinner…
This note is a response to recent challenge by showing basic mistakes in his conclusions. The proof is elementary, but leads to some fundamental results in correctly understanding an extensively studied problem in continuum mechanics.
To a singular foliation on the plane corresponds a circular boundary at infinity endowed with a pre-lamination on the circle. We solve the converse direction. We determine which pre-lamination on the circle are boundary at infinity of a…
We study a model for rate-dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor, and investigate the existence of global-in-time solutions to the related PDE system. We reveal its…
Deformation quantization conventionally is described in terms of multidifferential operators. Jet manifold technique is well-known provide the adequate formulation of theory of differential operators. We extended this formulation to the…
We construct a compact nonpositively curved squared 2-complex whose universal cover contains a flat plane that is not the limit of periodic flat planes.
This paper is concerned with an initial and boundary value problem of the one-dimensional planar MHD equations for viscous, heat-conducting, compressible, ideal polytropic fluids with constant transport coefficients and large data. The…
We consider the propagation of surface shear waves in a half-plane, whose shear modulus $\mu(y)$ and density $\rho(y)$ depend continuously on the depth coordinate $y$. The problem amounts to studying the parametric Sturm-Liouville equation…
We consider the global bifurcation problem for spatially periodic traveling waves for two-dimensional gravity-capillary vortex sheets. The two fluids have arbitrary constant, non-negative densities (not both zero), the gravity parameter can…
We apply Heegaard Floer homology to study deformations of singularities of plane algebraic curves. Our main result provides an obstruction to the existence of a deformation between two singularities. Generalizations include the case of…
Disordered many-particle hyperuniform systems are exotic amorphous states characterized by anomalous suppression of large-scale density fluctuations. Here we substantially broaden the hyperuniformity concept along four different directions.…
This Note determines the unsteady non-circulatory forces on an arbitrarily deforming panel with a Holder-continuous porosity distribution. An analytical expression for the non-circulatory pressure distribution is presented and evaluated for…
Stationary bifurcations in several nonlinear models of fluid conveying pipes fixed at both ends are analyzed with the use of Lyapunov-Schmidt reduction and singularity theory. Influence of gravitational force, curvature and vertical elastic…
The global existence of bounded solutions to reaction-diffusion systems with fractional diffusion in the whole space $\mathbb R^N$ is investigated. The systems are assumed to preserve the non-negativity of initial data and to dissipate…
Two questions related to elastic motions are raised and addressed. First: in which theoretical framework can the equations of motion be written for an elastic half-space put into uniform rotation? It is seen that nonlinear finite elasticity…
We survey various Alexander-type invariants of plane curve complements, with an emphasis on obstructions on the type of groups that can arise as fundamental groups of complements to complex plane curves. Also included are some new…