Global well-posedness for the 2 D quasi-geostrophic equation in a critical Besov space [PDF]
, 2006 We show that the the 2 D quasi-geostrophic equation has global and unique strong solution, when the (large) data belongs in the critical, scale invariant space $\dot{B}^{2-2\al}_{2, \infty}\cap L^{2/(2\al-1)}$
Stefanov, Atanas
core +3 more sources
The Zero Number Diminishing Property under General Boundary Conditions
, 2019 The so-called {\it zero number diminishing property} (or {\it zero number argument}) is a powerful tool in qualitative studies of one dimensional parabolic equations, which says that, under the zero- or non-zero-Dirichlet boundary conditions, the number ...
Lou, Bendong
core +1 more source
Existence and nonexistence of global solutions of degenerate and singular parabolic systems
, 2000 Abstract and Applied Analysis, Volume 5, Issue 4, Page 265-284, 2000.
Gabriella Caristi
wiley +1 more source
Self-propagating High temperature Synthesis (SHS) in the high activation energy regime [PDF]
, 2005 We derive the precise limit of SHS in the high activation energy scaling suggested by B.J. Matkowksy-G.I. Sivashinsky in 1978 and by A. Bayliss-B.J. Matkowksy-A.P. Aldushin in 2002. In the time-increasing case the limit turns out to be the Stefan problem
Monneau, Regis, Weiss, G. S.
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Study of the risk-adjusted pricing methodology model with methods of Geometrical Analysis
, 2010 Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM) incorporates both transaction costs and the risk from a volatile portfolio.
Bordag L.A. +11 more
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Well-posedness of a porous medium flow with fractional pressure in Sobolev spaces
, 2016 The nonnegative solution for a linear degenerate diffusion transport eqution is proved. As a result, we show the existence and uniqueness of the solution for the fractional porous medium equation in Sobolev spaces $H^\alpha$ with nonnegative initial data,
Xiao, Weiliang, Zhou, Xuhuan
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Optimal coupling for mean field limits
, 2009 We review recent quantitative results on the approximation of mean field diffusion equations by large systems of interacting particles, obtained by optimal coupling methods.
Bolley, François
core
Allen-Cahn and Cahn-Hilliard variational inequalities solved with Optimization Techniques [PDF]
, 2010 Parabolic variational inequalities of Allen-Cahn and Cahn- Hilliard type are solved using methods involving constrained optimization. Time discrete variants are formulated with the help of Lagrange multipliers for local and non-local equality and ...
Blank, Luise +4 more
core
The impact factors of the risk index and diffusive dynamics of a SIS free boundary model. [PDF]
Infect Dis Model, 2022 Tong Y, Ahn I, Lin Z.
europepmc +1 more source
Harnack's inequality for doubly nonlinear equations of slow diffusion type. [PDF]
Calc Var Partial Differ Equ, 2021 Bögelein V +3 more
europepmc +1 more source