[图书][B] Gradient flows: in metric spaces and in the space of probability measures
The book is devoted to the theory of gradient flows in the general framework of metric
spaces, and in the more specific setting of the space of probability measures, which provide …
spaces, and in the more specific setting of the space of probability measures, which provide …
Entropy dissipation methods for degenerate parabolicproblems and generalized sobolev inequalities
We analyse the large-time asymptotics of quasilinear (possibly) degenerate parabolic
systems in three cases: 1) scalar problems with confinement by a uniformly convex potential …
systems in three cases: 1) scalar problems with confinement by a uniformly convex potential …
[图书][B] Quasi-hydrodynamic semiconductor equations
A Jüngel - 2011 - books.google.com
In this book a hierarchy of macroscopic models for semiconductor devices is presented.
Three classes of models are studied in detail: isentropic drift-diffusion equations, energy …
Three classes of models are studied in detail: isentropic drift-diffusion equations, energy …
A family of nonlinear fourth order equations of gradient flow type
Global existence and long-time behavior of solutions to a family of nonlinear fourth order
evolution equations on R d are studied. These equations constitute gradient flows for the …
evolution equations on R d are studied. These equations constitute gradient flows for the …
The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation
We prove the global existence of non-negative variational solutions to the “drift diffusion”
evolution equation\partial_t u+ div\left (u D\left (2 Δ\sqrt u\sqrt uf\right)\right)= 0 under …
evolution equation\partial_t u+ div\left (u D\left (2 Δ\sqrt u\sqrt uf\right)\right)= 0 under …
Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model
G Galiano, ML Garzón, A Jüngel - Numerische Mathematik, 2003 - Springer
A positivity-preserving numerical scheme for a strongly coupled cross-diffusion model for
two competing species is presented, based on a semi-discretization in time. The variables …
two competing species is presented, based on a semi-discretization in time. The variables …
Long-Time Asymptotics for Strong Solutions¶ of the Thin Film Equation
JA Carrillo, G Toscani - Communications in mathematical physics, 2002 - Springer
In this paper we investigate the large-time behavior of strong solutions to the one-
dimensional fourth order degenerate parabolic equation ut=−(uu xxx) x, modeling the …
dimensional fourth order degenerate parabolic equation ut=−(uu xxx) x, modeling the …
A review on the quantum drift diffusion model
R Pinnau - Transport Theory and Statistical Physics, 2002 - Taylor & Francis
We consider the quantum drift diffusion model for semiconductor devices and collect recent
results on the stationary and transient equations. The stationary model including generation …
results on the stationary and transient equations. The stationary model including generation …
The Derrida–Lebowitz–Speer–Spohn equation: Existence, nonuniqueness, and decay rates of the solutions
The logarithmic fourth-order equation \partial_tu+\frac12i,j=1^dij^2(uij^2\logu)=0, called the
Derrida–Lebowitz–Speer–Spohn equation, with periodic boundary conditions is analyzed …
Derrida–Lebowitz–Speer–Spohn equation, with periodic boundary conditions is analyzed …
A positivity-preserving numerical scheme for a nonlinear fourth order parabolic system
A Jüngel - SIAM journal on numerical analysis, 2001 - SIAM
\noindent A positivity-preserving numerical scheme for a fourth order nonlinear parabolic
system arising in quantum semiconductor modeling is studied. The system is numerically …
system arising in quantum semiconductor modeling is studied. The system is numerically …