相关论文: On conserved Penrose-Fife type models

This work obtains a fixed-point equation for the solution of linear parabolic partial differential problems based on solutions to heat problems. This is a pointwise equality, so we have required non-standard techniques that involve the…

Based on Lie group method, potential symmetry and invariant solutions for generalized quasilinear hyperbolic equations are studied. To obtain the invariant solutions in explicit form, we focus on the physically interesting situations which…

This is a generalization of our prior work on the compact fixed point theory for the elliptic Rosseland-type equations. We obtain the maximum principle without the technical Steklov techniques. Inspired by the Rosseland equation in the…

We study the continuity of weak solutions for quasilinear elliptic systems with source terms of critical growth arising from a transport-energy structure. The latter occurs frequently in connection with the first balance principles of…

We study the local regularity of $p$-caloric functions or more generally of $\phi$-caloric functions. In particular, we study local solutions of non-linear parabolic systems with homogeneous right hand side, where the leading terms has…

This paper is concerned with the global existence and stability of solution to the quasi linear hyperbolic-parabolic chemotaxis system on the half-line,which was proposed in[1] to primarily describe the formation of coherent vascular…

Our study of a basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics in the case of constant but non-equal densities of the phases, begun by the first two authors is continued. We extend our…

We investigate a compressible two-fluid Navier-Stokes type system with a single velocity field and algebraic closure for the pressure law. The constitutive relation involves densities of both fluids through an implicit function. We are…

This paper provides a dynamical frame to study non-autonomous parabolic partial differential equations with finite delay. Assuming monotonicity of the linearized semiflow, conditions for the existence of a continuous separation of type II…

In this article we present several results concerning uniqueness of $C$-viscosity and $L_{p}$-viscosity solutions for fully nonlinear parabolic equations. In case of the Isaacs equations we allow lower order terms to have just measurable…

In this paper, we consider the Q-tensor model of nematic liquid crystals, which couples the Navier-Stokes equations with a parabolic-type equation describing the evolution of the directions of the anisotropic molecules, in the half-space.…

We show a result of maximal regularity in spaces of H\"older continuous function, concerning linear parabolic systems, with dynamic or Wentzell boundary conditions, with an elliptic diffusion term on the boundary.

Maximal $L^p$-$L^q$ regularity is proved for the strong, weak and very weak solutions of the inhomogeneous Stokes problem with Navier-type boundary conditions in a bounded domain $\Omega$, not necessarily simply connected. This extends…

In this paper, the one-dimensional compressible Navier-Stokes system with outer pressure boundary conditions is investigated. Under some suitable assumptions, we prove that the specific volume and the temperature are bounded from below and…

Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…

This article deals with a nonlocal Penrose-Fife type phase field system with inertial term. We do not know whether we can prove existence of solutions in reference to Colli--Grasselli--Ito [Electron. J. Differential Equations 2002, No. 100,…

In this article, we investigate the maximal smoothness (infinite differentiability) of solutions to thermoelastic models, specifically those where the heat equation is of the ``phase-lag'' or ``parabolic'' type. We derive optimal regularity…

We consider a p-system of conservation laws that emerges in one dimensional elasticity theory. Such system is determined by a function $W$, called strain-energy function. We consider four forms of $W$ which are known in the literature.…

In this paper we provide a local well posedness result for a quasilinear beam-wave system of equations on a one-dimensional spatial domain under periodic and Dirichlet boundary conditions. This kind of systems provides a refined model for…

Locally bounded, local weak solutions to a doubly nonlinear parabolic equation, which models the multi-phase transition of a material, is shown to be locally continuous. Moreover, an explicit modulus of continuity is given. The effect of…