Generation of analytic semi-groups in L2 for a class of second order degenerate elliptic operators
Generation of Interface for an Allen-Cahn Equation with Nonlinear Diffusion
In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to infinity: we prove a generation of interface property.
Geometrical properties of the solutions of one-dimensional nonlinear parabolic equations.
Global and blowup solutions of quasilinear parabolic equation with critical Sobolev equation and lower energy initial value.
Global and non-global existence of solutions to a nonlocal and degenerate quasilinear parabolic system
The paper deals with positive solutions of a nonlocal and degenerate quasilinear parabolic system not in divergence form with null Dirichlet boundary conditions. By using the standard approximation method, we first give a series of fine a priori estimates for the solution of the corresponding approximate problem. Then using the diagonal method, we get the local existence and the bounds of the solution to this problem. Moreover, a necessary and sufficient condition for the non-global existence...
Global attractor for a semilinear parabolic equation involving Grushin operator.
Global attractors for a class of degenerate diffusion equations.
Global Attractors for a Class of Semilinear Degenerate Parabolic Equations on
We prove the existence of global attractors for the following semilinear degenerate parabolic equation on : ∂u/∂t - div(σ(x)∇ u) + λu + f(x,u) = g(x), under a new condition concerning the variable nonnegative diffusivity σ(·) and for an arbitrary polynomial growth order of the nonlinearity f. To overcome some difficulties caused by the lack of compactness of the embeddings, these results are proved by combining the tail estimates method and the asymptotic a priori estimate method.
Global existence and asymptotic behaviour for a degenerate diffusive SEIR model.
Global existence and blow-up analysis for some degenerate and quasilinear parabolic systems.
Global existence and blow-up solutions and blow-up estimates for some evolution systems with -Laplacian with nonlocal sources.
Global existence and long-time behavior of solutions to a class of degenerate parabolic equations
We study the global existence and long-time behavior of solutions for a class of semilinear degenerate parabolic equations in an arbitrary domain.
Global existence for degenerate quadratic reaction-diffusion systems
Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in and space dimensions
Global existence of solutions to a chemotaxis system with volume filling effect
A system of quasilinear parabolic equations modelling chemotaxis and taking into account the volume filling effect is studied under no-flux boundary conditions. The resulting system is non-uniformly parabolic. A Lyapunov functional for the system is constructed. The proof of existence and uniqueness of regular global-in-time solutions is given in cases when either the Lyapunov functional is bounded from below or chemotactic forces are suitably weakened. In the first case solutions are uniformly...
Global Schauder estimates for a class of degenerate Kolmogorov equations
We consider a class of possibly degenerate second order elliptic operators on ℝⁿ. This class includes hypoelliptic Ornstein-Uhlenbeck type operators having an additional first order term with unbounded coefficients. We establish global Schauder estimates in Hölder spaces both for elliptic equations and for parabolic Cauchy problems involving . The Hölder spaces in question are defined with respect to a possibly non-Euclidean metric related to the operator . Schauder estimates are deduced by sharp...
Global weak solutions for a degenerate parabolic system modelling a one-dimensional compressible miscible flow in porous media
We show the solvability of a nonlinear degenerate parabolic system of two equations describing the displacement of one compressible fluid by another, completely miscible with the first, in a one-dimensional porous medium, neglecting the molecular diffusion. We use the technique of renormalised solutions for parabolic equations in the derivation of a priori estimates for viscosity type solutions. We pass to the limit, as the molecular diffusion coefficient tends to 0, on the parabolic system, owing...
Gradient estimates for a new class of degenerate elliptic and parabolic equations
Grandient Estimates for Degenerate Diffusion Equations. I.