Convergence to steady states in a viscous Hamilton-Jacobi equation with degenerate diffusion

This paper deals with weak solutions of the one-dimensional viscous Hamilton-Jacobi equation

     

Hyperbolic-parabolic singular perturbation for mildly degenerate Kirchhoff equations: Time-decay estimates

We consider the second order Cauchy problem

     

Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect

We consider the elliptic-parabolic PDE system

     

Nonresonant smoothing in Sobolev spaces for coupled wave+transport equations

Consider a system consisting of a linear wave equation coupled to a transport equation:

     

Perturbation results of critical elliptic equations of Caffarelli-Kohn-Nirenberg type

We find for small ε positive solutions to the equation

     

Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model

We consider the classical parabolic-parabolic Keller-Segel system

     

Global attractor for a model of extensible beam with nonlinear damping and source terms

This paper is concerned with the existence of a global attractor for the nonlinear beam equation, with nonlinear damping and source terms,

     

Global solutions for dissipative Kirchhoff strings with non-Lipschitz nonlinear term

We investigate the evolution problem

     

Exact multiplicity for boundary blow-up solutions

The singularly perturbed boundary blow-up problem

     

Positive solutions to nonlinear p-Laplace equations with Hardy potential in exterior domains

We study the existence and nonexistence of positive (super)solutions to the nonlinear p-Laplace equation

     

Concentration phenomena for the volume functional in unbounded domains: identification of concentration points

We study the variational problem

     

Initial blow-up of solutions of semilinear parabolic inequalities

We study classical nonnegative solutions u(x,t) of the semilinear parabolic inequalities