On the stochastic porous medium equation

By J. U. Kim. 2006

62 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/a21473ef85540d1ed7288e3355defbc105990061

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Wei Liu
2. Michael Röckner
3. Feng-Yu Wang
4. Wei David Liu
5. Benjamin Gess
6. Jiagang Ren
7. Patrick Cattiaux
8. Tusheng Zhang

In Computational Theory and Mathematics

1. Wei Liu
2. Michael Röckner
3. Wei David Liu
4. Feng-Yu Wang
5. Benjamin Gess
6. Xicheng Zhang
7. Jiagang Ren
8. Tusheng Zhang

In Finance

1. Wei Liu
2. Michael Röckner
3. Benjamin Gess
4. Feng-Yu Wang
5. Wei David Liu
6. Tusheng Zhang
7. Xicheng Zhang
8. Jiagang Ren

Citations in the corpus

• Harnack inequality and strong Feller property for stochastic fast-diffusion equations☆ (2007, background): “For more general stochastic evolution equations in Hilbert space we refer to [8, 12, 13, 14] and the references within.”
• Random attractors for a class of stochastic partial differential equations driven by general additive noise (2010, unknown): “46 41 v2 [ m at AMS Subject Classification: 35B41, 60H15, 37L30, 35B40 Keywords: Random attractor; Lévy noise; fractional Brownian motion; stochastic evolution equations; porous media equations; p-Laplace equation; reaction-diffusion equations.”
• Non-monotone stochastic generalized porous media equations☆ (2008, methodology): “By combining the Sobolev inequality with Galerkin approximations, Kim [10] was able to solve this equation on L(R; dx) for X0 ∈ L(R×Ω; dx×P), and the unique solution is an adapted process on L(R; dx) satisfying E ∫ T”
• Stochastic generalized porous media and fast diffusion equations (2006, background): “But also the case L = −(− ) , α ∈ (0, d2 ) ∩ (0,1], Λ = R is included (hence the cases studied in [11] are all covered by our results).”
• Strong Solutions for Stochastic Partial Differential Equations of Gradient Type (2011, methodology): “For the SPME with additive noise the same had been obtained in [Kim06].”
• Harnack inequality and applications for stochastic evolution equations with monotone drifts (2008, background): “This type of SPDE has been studied intensively in recent years, we refer to [8, 13, 20, 28, 18, 27, 39] (and references therein) for various generalizations and applications.”
• Martingale solutions and Markov selections for stochastic partial differential equations (2009, unknown): “in [12], [6], [19], [3], [4], [22], [20](see also [18]).”