32 citations · 70 across the 30 of their papers we have counts for
30 papers
The Moser method and boundedness of solutions to infinitely degenerate elliptic equations
Lyudmila Korobenko, Cristian Rios, Eric Sawyer +1
We show that if is equipped with certain non-doubling metric and an Orlicz-Sobolev inequality holds for a special family of Young functions , then weak solution…
The radiation theory of radial solutions to 3D energy critical wave equations
Ruipeng Shen
In this work we consider a wide range of energy critical wave equation in 3-dimensional space with radial data. We are interested in exterior scattering phenomenon, in which the as…
Classification of radial non-radiative solutions to the 5D nonlinear wave equations
Liang Li, Ruipeng Shen, Chenhui Wang
In this work we classify all radial non-radiative solutions to the 5D nonlinear wave equations with a wide range of energy critical nonlinearity. We show that such a solution alway…
Radiation fields and non-radiative solutions to the energy sub-critical wave equations
Liang Li, Ruipeng Shen, Chenhui Wang
Radiation field and channel of energy method have become important tools in the study of nonlinear wave equations in recent years. In this work we give basic theory of radiation fi…
Asymptotic behaviour of non-radiative solution to the wave equations
Liang Li, Ruipeng Shen, Chenhui Wang +1
In this work we consider weakly non-radiative solutions to both linear and non-linear wave equations. We first characterize all weakly non-radiative free waves, without the radial…
An inequality regarding non-radiative linear waves via a geometric method
Liang Li, Ruipeng Shen, Chenhui Wang
In this work we consider the operator \[ (\mathbf{T} G) (x)= \int_{\mathbb{S}^2} G(x\cdot ω, ω) dω, \quad x\in \mathbb{R}^3, \; G\in L^2(\mathbb{R}\times \mathbb{S}^2). \] This is…
Energy distribution of solutions to defocusing semi-linear wave equation in higher dimensional space
Liang Li, Ruipeng Shen
The topic of this paper is a semi-linear, defocusing wave equation in sub-conformal case in the higher dimensional space whose initial data are radical an…
Explicit formula of radiation fields of free waves with applications on channel of energy
Liang Li, Ruipeng Shen, Lijuan Wei
In this work we give a few explicit formulas regarding the radiation fields of linear free waves. We then apply these formulas on the channel of energy theory. We characterize all…
Energy Distribution of solutions to defocusing semi-linear wave equation in two dimensional space
Liang Li, Ruipeng Shen, Lijuan Wei
We consider finite-energy solutions to the defocusing nonlinear wave equation in two dimensional space. We prove that almost all energy moves to the infinity at almost the light sp…
Exterior scattering of non-radial solutions to energy subcritical wave equations
Ruipeng Shen
We consider the defocusing, energy subcritical wave equation in dimension and prove the exterior scattering of solutions if $…
Asymptotic energy distribution of one-dimensional nonlinear wave equation
Ruipeng Shen
In this work we consider the defocusing nonlinear wave equation in one-dimensional space. We show that almost all energy is located near the light cone as time tends to i…
Weakly non-radiative radial solutions to 3D energy subcritical wave equations
Ruipeng Shen
In this work we consider the energy subcritical 3D wave equation and discuss its (weakly) non-radiative solutions, i.e. the solutions define…
Scattering theory for subcritical wave equation with inverse square potential
Changxing Miao, Ruipeng Shen, Tengfei Zhao
We consider the scattering theory for the defocusing energy subcritical wave equations with an inverse square potential. By employing the energy flux method we establish energy flu…
Long time behaviour of finite-energy radial solutions to energy subcritical wave equation in higher dimensions
Ruipeng Shen
We consider the defocusing, energy subcritical wave equation in 4 to 6 dimensional spaces with radial initial data. We define …
Inward/outward Energy Theory of Wave Equation in Higher Dimensions
Ruipeng Shen
We consider the semi-linear, defocusing wave equation in with . We generalize the inward/outward en…
Inward/outward Energy Theory of Non-radial Solutions to 3D Semi-linear Wave Equation
Ruipeng Shen
The topic of this paper is a semi-linear, energy sub-critical, defocusing wave equation in the 3-dimensional space with . We gener…
Scattering of solutions to NLW by Inward Energy Decay
Ruipeng Shen
The topic of this paper is a semi-linear, energy sub-critical, defocusing wave equation in the 3-dimensional space () whose initia…
Morawetz Estimates Method for Scattering of Radial Energy Sub-critical Wave Equation
Ruipeng Shen
In this short paper we consider a semi-linear, energy sub-critical, defocusing wave equation in the 3-dimensional space with . W…
Energy Distribution of Radial Solutions to Energy Subcritical Wave Equation with an Application on Scattering Theory
Ruipeng Shen
The topic of this paper is a semi-linear, energy sub-critical, defocusing wave equation in the 3-dimensional space () whose initia…
Continuity of weak solutions to rough infinitely degenerate equations
Lyudmila Korobenko, Cristian Rios, Eric Sawyer +1
We obtain a generalization of the DeGiorgi Lemma to the infinitely degenerate regime and apply it to obtain continuity of weak solutions to certain infinitely degenerate equations.…
Sharp local boundedness and maximum principle in the infinitely degenerate regime via DeGiorgi iteration
Lyudmila Korobenko, Cristian Rios, Eric Sawyer +1
We obtain local boundedness and maximum principles for weak subsolutions to certain infinitely degenerate elliptic divergence form equations, and the local boundedness turns out to…
Scattering of solutions to the defocusing energy sub-critical semi-linear wave equation in 3D
Ruipeng Shen
In this paper we consider a semi-linear, energy sub-critical, defocusing wave equation in the 3-dimensional space with . We prov…
Bounded Solutions to an Energy Subcritical Non-linear Wave Equation on R^3
Ruipeng Shen
In this work we consider an energy subcritical semi-linear wave equation () \[ \partial_t^2 u - Δu = ϕ(x) |u|^{p-1} u, \qquad (x,t) \in {\mathbb R}^3 \times {\mathbb R}…
Local boundedness, maximum principles, and continuity of solutions to infinitely degenerate elliptic equations
Lyudmila Korobenko, Cristian Rios, Eric Sawyer +1
We develop subrepresentation inequalities for infinitely degenerate metrics, and obtain corresponding Poincare and Sobolev inequalities. We then derive conditions on the degenerate…