Nonlinear anisotropic degenerate parabolic-hyperbolic equations with stochastic forcing

Pang, Peter H. C.

doi:10.1016/j.jfa.2021.109222

Cited by 7 publications

(2 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, a blow-up criterion is also obtained. We refer to [11,19,42] for the study about the dependence on the initial data for cases that solutions to the target problems exist globally. However, it is necessary to point out that almost nothing is known on the analysis for dependence on initial data for SPDEs whose solutions may blow up in finite time.…”

Section: Main Results and Remarksmentioning

confidence: 99%

Well-posedness for a stochastic Camassa–Holm type equation with higher order nonlinearities

Miao

Rohde

Tang

2023

Stoch PDE: Anal Comp

View full text Add to dashboard Cite

This paper aims at studying a generalized Camassa–Holm equation under random perturbation. We establish a local well-posedness result in the sense of Hadamard, i.e., existence, uniqueness and continuous dependence on initial data, as well as blow-up criteria for pathwise solutions in the Sobolev spaces $$H^s$$ H s with $$s>3/2$$ s > 3 / 2 for $$x\in \mathbb R$$ x ∈ R . The analysis on continuous dependence on initial data for nonlinear stochastic partial differential equations has gained less attention in the literature so far. In this work, we first show that the solution map is continuous. Then we introduce a notion of stability of exiting time. We provide an example showing that one cannot improve the stability of the exiting time and simultaneously improve the continuity of the dependence on initial data. Finally, we analyze the regularization effect of nonlinear noise in preventing blow-up. Precisely, we demonstrate that global existence holds true almost surely provided that the noise is strong enough.

show abstract

Section: Main Results and Remarksmentioning

confidence: 99%

Well-posedness for a stochastic Camassa–Holm type equation with higher order nonlinearities

Miao

Rohde

Tang

2023

Stoch PDE: Anal Comp

View full text Add to dashboard Cite

show abstract

“…In [2] (see also [5]), the authors derived some basic quantitative compactness estimates. These n-uniform estimates, which were used and further refined in [9,10] and [3], take the form…”

Section: Introductionmentioning

confidence: 99%