Asymptotic behavior of solutions for a semibounded nonmonotone evolution equation.
Asymptotic behavior of solutions of a semilinear heat equation with subcritical nonlinearity
Asymptotic behavior of solutions to a reaction-diffusion system with a cross diffusion matrix on unbounded domains.
Asymptotic behaviour of solutions of some semilinear parabolic problems
Asymptotic behaviour of solutions to nonlinear parabolic equations with variable viscosity and geometric terms.
Asymptotic Behaviour of the Solution of a Semilinear Parabolic Equation.
Asymptotic behaviour of the solutions of a strongly nonlinear parabolic problem
Asymptotic Expansions for the Solutions of Certain Nonlinear Parabolic Problems. I .
Asymptotic integration of parabolic problems with large high-frequency summands.
Asymptotics for conservation laws involving Lévy diffusion generators
Let -ℒ be the generator of a Lévy semigroup on L¹(ℝⁿ) and f: ℝ → ℝⁿ be a nonlinearity. We study the large time asymptotic behavior of solutions of the nonlocal and nonlinear equations uₜ + ℒu + ∇·f(u) = 0, analyzing their -decay and two terms of their asymptotics. These equations appear as models of physical phenomena that involve anomalous diffusions such as Lévy flights.
Asymptotics for large time of solutions to nonlinear system associated with the penetration of a magnetic field into a substance
The nonlinear integro-differential system associated with the penetration of a magnetic field into a substance is considered. The asymptotic behavior as of solutions for two initial-boundary value problems are studied. The problem with non-zero conditions on one side of the lateral boundary is discussed. The problem with homogeneous boundary conditions is studied too. The rates of convergence are given. Results presented show the difference between stabilization characters of solutions of these...
Asymptotics of parabolic equations with possible blow-up
We describe the long-time behaviour of solutions of parabolic equations in the case when some solutions may blow up in a finite or infinite time. This is done by providing a maximal compact invariant set attracting any initial data for which the corresponding solution does not blow up. The abstract result is applied to the Frank-Kamenetskii equation and the N-dimensional Navier-Stokes system with small external force.
Attractors for a class of doubly nonlinear parabolic systems.
Attractors of asymptotically periodic multivalued dynamical systems governed by time-dependent subdifferentials.
Attractors of nonautonomous and stochastic differential inclusions
Behaviour of solutions to as p → +∞
Bifurcation points of reaction-diffusion systems with unilateral conditions
Bifurcations for Turing instability without SO(2) symmetry
In this paper, we consider the Swift–Hohenberg equation with perturbed boundary conditions. We do not a priori know the eigenfunctions for the linearized problem since the symmetry of the problem is broken by perturbation. We show that how the neutral stability curves change and, as a result, how the bifurcation diagrams change by the perturbation of the boundary conditions.
Bifurcations of finite difference schemes and their approximate inertial forms
Bistable traveling waves for monotone semiflows with applications
This paper is devoted to the study of traveling waves for monotone evolution systems of bistable type. In an abstract setting, we establish the existence of traveling waves for discrete and continuous-time monotone semiflows in homogeneous and periodic habitats. The results are then extended to monotone semiflows with weak compactness. We also apply the theory to four classes of evolution systems.