Related papers: Descret Solution for a Nonlinear Parabolic Equatio…
The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear) porous medium equation with blow-up term and nondecreasing constraint. To this end, the equation, arising in the context of Damage…
We prove in this paper the existence of solutions of nonlinear parabolic problems in inhomogeneous Musielak Orlicz Sobolev spaces, we assume neither a $\Delta_2$ nor $\nabla_2$ on the Musielak function $\varphi$. The main contribution of…
We study the two-dimensional Muskat problem in a horizontally periodic setting and for fluids with arbitrary densities and viscosities. We show that in the presence of surface tension effects the Muskat problem is a quasilinear parabolic…
This paper is devoted to the analysis of non-negative solutions for a degenerate parabolic-elliptic Patlak-Keller-Segel system with critical nonlinear diffusion in a bounded domain with homogeneous Neumann boundary conditions. Our aim is to…
We consider an abstract first order evolution equation in a Hilbert space in which the linear part is represented by a self-adjoint nonnegative operator A with discrete spectrum, and the nonlinear term has order greater than one at the…
We construct an example of a one-dimensional parabolic integro-differential equation with nonlocal diffusion which does not have asymptotically finite-dimensional dynamics in the corresponding state space. This example is more natural in…
We study the behaviour of solutions of linear non-autonomous parabolic equations subject to Dirichlet or Neumann boundary conditions under perturbation of the domain. We prove that Mosco convergence of function spaces for non-autonomous…
We find an explicit form of weak solutions to a Riemann problem for a degenerate semilinear parabolic equation with piecewise constant diffusion coefficient. It is demonstrated that the phase transition lines (free boundaries) correspond to…
We give a means for measuring the equation of evolution of a complex scalar field that is known to obey an otherwise unspecified (2+1)-dimensional dissipative nonlinear parabolic differential equation, given field moduli over three…
In this contribution we prove the existence of weak solutions to degenerate parabolic systems arising from the coupled moisture movement, transport of dissolved species and heat transfer through partially saturated porous materials.…
Under a precise nonlinearity-diffusivity condition we establish the decay of space-periodic entropy solutions of a multidimensional degenerate nonlinear parabolic equation.
We study convergence of the evolving finite element semi-discretization of a parabolic partial differential equation on an evolving bulk domain. The boundary of the domain evolves with a given velocity, which is then extended to the bulk by…
We considered classical solutions to the initial boundary value problem for non-isentropic compressible Euler equations with damping in multi-dimensions. We obtained global a priori estimates and global existence results of classical…
We consider a class of doubly nonlinear degenerate hyperbolic-parabolic equations with homogeneous Dirichlet boundary conditions, for which we first establish the existence and uniqueness of entropy solutions. We then turn to the…
We consider a Cauchy Dirichlet problem for a quasilinear second order parabolic equation with lower order term driven by a singular coefficient. We establish an existence result to such a problem and we describe the time behavior of the…
In this paper we consider the numerical approximation of a general second order semi-linear parabolic partial differential equation. Equations of this type arise in many contexts, such as transport in porous media. Using finite element…
This paper is concerned with the analysis of a new stable space-time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on…
We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as a natural generalization of the semilinear reaction-diffusion equation with dynamic boundary conditions. The corresponding class of…
We study the well-posedness of solutions to the general nonlinear parabolic equations with merely integrable data in time-dependent Musielak-Orlicz spaces. With the help of a density argument, we establish the existence and uniqueness of…
We analyze a quasi-static Biot system of poroelasticity for both compressible and incompressible constituents. The main feature of this model is a nonlinear coupling of pressure and dilation through the system's permeability tensor. Such a…