Related papers: Bifurcation curves of a diffusive logistic equatio…
We study the one-dimensional Kirchhoff type equation $$ -(b + a\Vert u'\Vert^{2}) u''(x) = \lambda u(x)^p, x \in I:= (-1,1), \enskip u(x) > 0, \enskip x\in I, \enskip u(\pm 1) = 0, $$ where $\Vert u'\Vert = \left(\int_I u'(x)^2…
Local bifurcation theory typically deals with the response of a degenerate but isolated equilibrium state or periodic orbit of a dynamical system to perturbations controlled by one or more independent parameters, and characteristically uses…
We perform a bifurcation analysis of the steady states of Rayleigh--B\'enard convection with no-slip boundary conditions in two dimensions using a numerical method called deflated continuation. By combining this method with an…
We study Hopf bifurcation from traveling-front solutions in the Cahn-Hilliard equation. The primary front is induced by a moving source term. Models of this form have been used to study a variety of physical phenomena, including pattern…
Analysis of non-compact manifolds almost always requires some controlled behavior at infinity. Without such, one neither can show, nor expect, strong properties. On the other hand, such assumptions restrict the possible applications and…
In this paper, we mainly discuss asymptotic profiles of solutions to a class of abstract second-order evolution equations of the form $u''+Au+u'=0$ in real Hilbert spaces, where $A$ is a nonnegative selfadjoint operator. The main result is…
Growth-induced instabilities are ubiquitous in biological systems and lead to diverse morphologies in the form of wrinkling, folding, and creasing. The current work focusses on the mechanics behind growth-induced wrinkling instabilities in…
We generalize the diffusion-limited aggregation by issuing many randomly-walking particles, which stick to a cluster at the discrete time unit providing its growth. Using simple combinatorial arguments we determine probabilities of…
In this paper we construct a family of exact strong solutions to the two-dimensional incompressible liquid crystal equations with finite energy. The initial velocity is chosen to be rotationally symmetric and the image of the initial…
In this article, we study about the solutions of second order linear differential equations by considering several conditions on the coefficients of homogenous linear differential equation and its associated non-homogenous linear…
Decay to asymptotic steady state in one-dimensional logistic-like mappings is characterized by considering a phenomenological description supported by numerical simulations and confirmed by a theoretical description. As the control…
A saddle-node bifurcation cascade is studied in the logistic equation, whose bifurcation points follow an expression formally identical to the one given by Feigenbaum for period doubling cascade. The Feigenbaum equation is generalized…
We show that there exist solutions of drift-diffusion equations in two dimensions with divergence-free super-critical drifts, that become discontinuous in finite time. We consider classical as well as fractional diffusion. However, in the…
We consider a Dirichlet type problem for a nonlinear, nonlocal equation driven by the degenerate fractional p-Laplacian, with a logistic type reaction depending on a positive parameter. In the subdiffusive and equidiffusive cases, we prove…
For ordinary (independent) percolation on a large class of lattices it is well known that below the critical percolation parameter $p_c$ the cluster size distribution has exponential decay and that power-law behavior of this distribution…
We study a class of nonlocal reaction-diffusion equations with a harvesting term where the nonlocal operator is given by a Bernstein function of the Laplacian. In particular, it includes the fractional Laplacian, fractional relativistic…
Diffusion-Limited Aggregation (DLA), the canonical model for non-equilibrium fractal growth, emerges from the simple rule of irreversible attachment by random walkers. Despite four decades of study, a unified computational framework…
We study local bifurcation from an eigenvalue with multiplicity greater than one for a class of semilinear elliptic equations. We evaluate the exact number of bifurcation branches of non trivial solutions and we compute the Morse index of…
We consider two cases of the so-called stick percolation model with sticks of length $L.$ In the first case, the orientation is chosen independently and uniformly, while in the second all sticks are oriented along the same direction. We…
An analytical study on crease formations in a swelling gel layer is conducted. By exploring the smallness of the layer thickness and using a method of coupled series-asymptotic expansions, the original nonlinear eigenvalue problem of…