Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption

We consider the Cauchy problem for the damped wave equation with absorption

(∗)     

Asymptotically self-similar solutions of the damped wave equation

We consider the damped hyperbolic equation

(1)     

Damped wave equation in the subcritical case

We study large time asymptotics of small solutions to the Cauchy problem for the one dimensional nonlinear damped wave equation

(1)     

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

We consider the second order Cauchy problem

     

Multiplicity of solutions to uniformly elliptic fully nonlinear equations with concave-convex right-hand side

We deal with existence, non-existence and multiplicity of solutions to the model problem

(P)     

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

     

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

We find for small ε positive solutions to the equation

     

Nonresonant smoothing in Sobolev spaces for coupled wave+transport equations

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

     

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

     

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

We consider the classical parabolic-parabolic Keller-Segel system

     

Initial blow-up of solutions of semilinear parabolic inequalities

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

     

On the Cauchy problem for a reaction-diffusion equation with a singular nonlinearity

We consider the following Cauchy problem with a singular nonlinearity

(P)

     

Homogenization limit of a parabolic equation with nonlinear boundary conditions

Consider the parabolic equation

(E)     

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,

     

The existence and decay of solutions of a damped Kirchhoff-Carrier equation in Banach spaces

This paper is concerned with the study of the existence and decay of solutions of the following initial value problem:

(∗)     

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

We consider the elliptic-parabolic PDE system

     

Regularity of invariant sets in semilinear damped wave equations

Under fairly general assumptions, we prove that every compact invariant subset I of the semiflow generated by the semilinear damped wave equation

     

Initial blow-up rates and universal bounds for nonlinear heat equations

We establish a universal upper bound on the initial blow-up rate for all positive classical solutions of the Dirichlet problem for the nonlinear heat equation