相关论文: Uniqueness of post-gelation solutions of a class o…
We study an infinite system of ordinary differential equations that models the evolution of coagulating and fragmenting clusters, which we assume to be composed of identical units. Under very mild assumptions on the coefficients we prove…
We study a homogenisation problem for problems of mixed type in the framework of evolutionary equations. The change of type is highly oscillatory. The numerical treatment is done by a discontinuous Galerkin method in time and a continuous…
The flow equation approach is a robust framework applicable to a broad class of singular SPDEs, including those with fractional Laplacians, throughout the entire subcritical regime. Inspired by Wilson's renormalization group, this method…
We present a simple unifying model for crystallization and melting temperatures by showing that homogeneous nucleation and phase transformations driven by thickening of pre-existing surface layers are limiting conditions of the more general…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
We consider a strongly nonlinear PDE system describing solid-solid phase transitions in shape memory alloys. The system accounts for the evolution of an order parameter (related to different symmetries of the crystal lattice in the phase…
Simple statistical agglomeration models can provide a universal link between the local structure and the glass transition temperature in network glasses. We first stress the physical features of the models and the hypothesis made, and then…
This work is devoted to the study of the initial boundary value problem for a general non isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985), which can be used as a phase transition model. We distinguish two cases,…
In this article, the uniqueness of weak solutions to the continuous coagulation and multiple fragmentation equation is proved for a large range of unbounded coagulation and multiple fragmentation kernels. The multiple fragmentation kernels…
Using continuation methods and bifurcation theory, we study the exact multiplicity of periodic solutions, and the global solution structure, for three classes of periodically forced equations with singularities, including the equations…
We consider the approach to self-similarity (or dynamical scaling) in Smoluchowski's equations of coagulation for the solvable kernels $K(x,y)=2$, $x+y$ and $xy$. In addition to the known self-similar solutions with exponential tails, there…
In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a…
In this paper we study a model for phase segregation consisting in a sistem of a partial and an ordinary differential equation. By a careful definition of maximal solution to the latter equation, this system reduces to an Allen-Cahn…
This article presents the study of a multi-species fluid characterised by a freeze-out or break-away of one or more species. Whereas single-fluid approximation suffices for modelling of the pre {\it freeze-out} period, multi-fluid…
Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient $(1+1)$-dimensional nonlinear diffusion-convection equations of the general form…
A global existence theorem on weak solutions is shown for the continuous coagulation equation with collisional breakage under certain classes of unbounded collision kernels and distribution functions. This model describes the dynamics of…
We study the global existence of a unique strong solution and its large-time behavior of a two-phase fluid system consisting of the compressible isothermal Euler equations coupled with compressible isentropic Navier-Stokes equations through…
The strong friction regime at low temperatures is analyzed systematically starting from the formally exact path integral expression for the reduced dynamics. This quantum Smoluchowski regime allows for a type of semiclassical treatment in…
In concentrated electrolytes with asymmetric or irregular ions, such as ionic liquids and solvent-in-salt electrolytes, ion association is more complicated than simple ion-pairing. Large branched aggregates can form at significant…
Thermodynamical properties of nuclear matter undergoing multifragmentation are studied within a simplified version of the statistical model. An exact analytical solution has been found for the grand canonical ensemble. Excluded volume…