Related papers: Global mild solutions for a transport-diffusion eq…
A mild formulation for stochastic parabolic Anderson model with time-homogeneous Gaussian potential suggests a way of defining a solution to obtain its optimal regularity. Two different interpretations in the equation or in the mild…
This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability…
In this paper, we construct global distributional solutions to the volume-preserving mean-curvature flow using a variant of the time-discrete gradient flow approach proposed independently by Almgren, Taylor and Wang (SIAM J. Control Optim.…
In [1], the Authors rigorously establish the relaxation limit from the Quantum Navier Stokes Poisson (QNSP) system to the Quantum Drift Diffusion (QDD) equation, while providing only a brief outline of the global existence theory for weak…
This paper focuses on a drift-diffusion system subjected to boundedly non dissipative Robin boundary conditions. A general existence result with large initial conditions is established by using suitable L1, L2 and trace estimates. Finally,…
We present generalized Green-Kubo expressions for thermal transport coefficients $\mu$ in non-conservative fluid-type systems, of the generic form, $\mu$ $= \mu_\infty$ $+\int^\infty_0 dt V^{-1} \av{I_\epsilon \exp(t {\cal L}) I}_0$ where…
We consider the numerical solution of time-dependent space tempered fractional diffusion equations. The use of Crank-Nicolson in time and of second-order accurate tempered weighted and shifted Gr\"unwald difference in space leads to dense…
This dissertation resolves a longstanding discussion of a mathematical problem important in contaminant hydrogeology and chemical-reaction engineering, the proper mathematical description for a miscible solute undergoing longitudinal…
The Swift-Hohenberg equation with dispersion is considered. Traveling wave solutions of the Swift-Hohenberg equation with dispersion are presented. The classification of these solutions is given. It is shown that the Swift-Hohenberg…
Mass transport problems are ubiquitous in diverse fields of physics and engineering. With the development of fractional calculus, many have taken to studying problems of fractional mass transport either through numerical simulations or…
One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…
We give a sufficient condition for blow up of positive mild solutions to an initial value problem for a nonautonomous weakly coupled system with distinct fractional diffusions. The proof is based on the study of blow up of a particular…
In this paper, we present splitting algorithms to solve multicomponent transport models with Maxwell-Stefan-diffusion approaches. The multicomponent models are related to transport problems, while we consider plasma processes, in which the…
The aim of this work is to study the global existence of solutions for some coupled systems of reaction diffusion which describe the spread within a population of infectious disease. We consider a triangular matrix diffusion and we show…
We construct a continuous semigroup of weak, dissipative solutions to a nonlinear partial differential equations modeling nematic liquid crystals. A new distance functional, determined by a problem of optimal transportation, yields sharp…
An effective theory for the soft field modes in hot QCD has been obtained recently by integrating out the field modes of momenta of order T and g T. The mean hard particle distribution obeys a transport equation with a collision term. The…
Transport theory is an efficient approach to derive an effective theory for the soft modes of QCD at high temperature. It is known that the leading order operators of this theory can be obtained from (semi-classical) kinetic equations of…
In this paper, we study the existence and uniqueness of mild solution for a stochastic neutral partial functional integro-differential equation with delay in a Hilbert space driven by a fractional Brownian motion and with non-deterministic…
We study controlled differential equations driven by a rough path (in the sense of T. Lyons) with an additional, possibly unbounded drift term. We show that the equation induces a solution flow if the drift grows at most linearly.…
A generalisation of reaction diffusion systems and their travelling solutions to cases when the productive part of the reaction happens only on a surface in space or on a line on plane but the degradation and the diffusion happen in bulk…