On a stochastic scalar conservation law

By J. U. Kim. 2003

103 citations recorded by the source corpus.

Subfields: Applied Mathematics, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/78fe5e67d8e4e55061622d2155f4cc3c2f4cfa43

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. Martina Hofmanov'a
2. Panagiotis E. Souganidis
3. Benjamin Gess
4. Julien Vovelle
5. Arnaud Debussche
6. Massimiliano Gubinelli
7. Samy Tindel
8. A. Deya

In Finance

1. Benjamin Gess
2. Panagiotis E. Souganidis
3. Samy Tindel
4. Martina Hofmanov'a
5. Massimiliano Gubinelli
6. A. Deya
7. Martin Hairer
8. David Nualart

In Modeling and Simulation

1. Samy Tindel
2. Arnaud Debussche
3. Kenneth Hvistendahl Karlsen
4. Martina Hofmanov'a
5. Jin Feng
6. Caroline Bauzet
7. Massimiliano Gubinelli
8. Panagiotis E. Souganidis

Citations in the corpus

• A priori estimates for rough PDEs with application to rough conservation laws (2016, background): “1), further developed in the stochastic setting in [2,5,21,48,62].”
• Stochastic scalar conservation laws (2008, background): “Kim [8] modifies deterministic arguments to construct a very special SPDE which is essentially reformulated as a randomness in coefficients type of conservation law.”
• On Nonlinear Stochastic Balance Laws (2011, background): “For σ = σ(t, x) in Ct(W 1,∞ x ) and with compact support in x, Kim [12] established the existence and uniqueness of entropy solutions in the one-dimensional case; see also [22].”
• Degenerate parabolic stochastic partial differential equations: Quasilinear case (2013, background): “Quasilinear degenerate parabolic stochastic partial differential equation, kinetic formulation, kinetic solution.”
• Scalar conservation laws with stochastic forcing (2010, methodology): “[ Kim03 , VW10], in particular concerning the study of the deterministic inviscid Burgers equation with random initial datum.”
• The Dirichlet problem for a conservation law with a multiplicative stochastic perturbation (2014, methodology): “Kim [24] proposed a method of compensated compactness to prove, via vanishing viscosity approximation, the existence of a stochastic weak entropy solution to the Cauchy problem.”
• THE CAUCHY PROBLEM FOR CONSERVATION LAWS WITH A MULTIPLICATIVE STOCHASTIC PERTURBATION (2012, methodology): “In the paper of Kim [14] a method of compensated compactness is used to prove, via vanishing viscosity approximation, existence of a stochastic weak entropy solution to the Cauchy problem du+ f(u)xdt = h(t, x)dw in ]0, T [×R.”
• Degenerate parabolic stochastic partial differential equations (2013, background): “Such a term can be used for instance to account for numerical and empirical uncertainties and therefore stochastic conservation laws has been recently of growing interest, see [6], [16], [20], [36], [44], [70], [76], [78].”
• Long‐Time Behavior, Invariant Measures, and Regularizing Effects for Stochastic Scalar Conservation Laws (2014, methodology): “For stochastic scalar conservation laws driven by additive noise, also including boundary value problems, we refer to the works by E, Khanin, Mazel and Sinai [22], Kim [37], Nakazawa [45], Saussereau and Stoica [51] and Vallet and Wittbold [53] and the references therein.”