Local Well-Posedness to the Cauchy Problem for an Equation of the Nagumo Type [PDF]
The Scientific World Journal, 2022 In this paper, we show the local well-posedness for the Cauchy problem for the equation of the Nagumo type in this equation (1) in the Sobolev spaces Hsℝ. If D>0, the local well-posedness is given for s>1/2 and for s>3/2 if D=0.
Vladimir Lizarazo +2 more
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Local Well-Posedness for Free Boundary Problem of Viscous Incompressible Magnetohydrodynamics
Mathematics, 2021 In this paper, we consider the motion of incompressible magnetohydrodynamics (MHD) with resistivity in a domain bounded by a free surface. An electromagnetic field generated by some currents in an external domain keeps an MHD flow in a bounded domain. On
Kenta Oishi, Yoshihiro Shibata
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Evolutionary dynamics on a regular networked structured and unstructured multi‐population
International Journal of Robust and Nonlinear Control, EarlyView., 2023 Abstract In this paper, we study collective decision‐making in a multi‐population framework, where groups of individuals represent whole populations that interact by means of a regular network. Each group consists of a number of players and every player can choose between two options.
Wouter Baar +2 more
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Well posedness of magnetohydrodynamic equations in 3D mixed-norm Lebesgue space
Open Mathematics, 2022 In this paper, we introduce a new metric space called the mixed-norm Lebesgue space, which allows its norm decay to zero with different rates as ∣x∣→∞| x| \to \infty in different spatial directions.
Liu Yongfang, Zhu Chaosheng
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A Class of Sixth Order Viscous Cahn-Hilliard Equation with Willmore Regularization in ℝ3
Mathematics, 2020 The main purpose of this paper is to study the Cauchy problem of sixth order viscous Cahn–Hilliard equation with Willmore regularization. Because of the existence of the nonlinear Willmore regularization and complex structures, it is difficult to obtain ...
Xiaopeng Zhao, Ning Duan
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Local Well-Posedness for the Magnetohydrodynamics in the Different Two Liquids Case
Mathematics, 2022 We consider the free boundary problem of MHD in the multi-dimensional case. This problem describes the motion of two incompressible fluids separated by a closed interface under the action of a magnetic field.
Elena Frolova, Yoshihiro Shibata
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On the two-dimensional singular stochastic viscous nonlinear wave equations
Comptes Rendus. Mathématique, 2022 We study the stochastic viscous nonlinear wave equations (SvNLW) on $\mathbb{T}^2$, forced by a fractional derivative of the space-time white noise $\xi $.
Liu, Ruoyuan, Oh, Tadahiro
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Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling [PDF]
Mathematica Bohemica, 2022 Global well-posedness for the Klein-Gordon-Schrödinger system with generalized higher order coupling, which is a system of PDEs in two variables arising from quantum physics, is proven.
Agus Leonardi Soenjaya
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Local Well-Posedness of a Two-Component Novikov System in Critical Besov Spaces
Mathematics, 2022 In this paper, we establish the local well-posedness for a two-component Novikov system in the sense of Hadamard in critical Besov spaces Bp,11+1p(R)×Bp,11+1p(R),1 ...
Min Guo, Fang Wang, Shengqi Yu
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On the Study of Local Solutions for a Generalized Camassa-Holm Equation
Abstract and Applied Analysis, 2012 The pseudoparabolic regularization technique is employed to study the local well-posedness of strong solutions for a nonlinear dispersive model, which includes the famous Camassa-Holm equation. The local well-posedness is established in the Sobolev space
Meng Wu
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