Geometric optics with critical vanishing viscosity for one-dimensional semilinear initial value problems.
Global Bifurcation of Waves.
Global convergence toward traveling fronts in nonlinear parabolic systems with a gradient structure
Global existence and blow up of solutions for a completely coupled Fujita type system of reaction-diffusion equations
We examine the parabolic system of three equations - Δu = , - Δv = , - Δw = , x ∈ , t > 0 with p, q, r positive numbers, N ≥ 1, and nonnegative, bounded continuous initial values. We obtain global existence and blow up unconditionally (that is, for any initial data). We prove that if pqr ≤ 1 then any solution is global; when pqr > 1 and max(α,β,γ) ≥ N/2 (α, β, γ are defined in terms of p, q, r) then every nontrivial solution exhibits a finite blow up time.
Global existence and large time asymptotic bounds of solutions of thermal diffusive combustion systems on
Global existence for a system of nonlocal PDEs with applications to chemically reacting incompressible fluids
We show global existence for a class of models of fluids that change their properties depending on the concentration of a chemical. We allow that the stress tensor in (t, x) depends on the velocity and concentration at other points and times. The example we have in mind foremost are materials with memory.
Global existence for degenerate quadratic reaction-diffusion systems
Global existence of solutions in invariant regions for reaction-diffusion systems with a balance law and a full matrix of diffusion coefficients.
Global existence versus blow up for some models of interacting particles
We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and Debye-Hückel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and oscillating complex-valued initial data, using a method due to S. Montgomery-Smith.