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THE SOBOLEV REGULARITY OF SOLUTIONS OF FIRST ORDER NONLINEAR EQUATIONS
Kang, Seongjoo Chungcheong Mathematical Society 2014 충청수학회지 Vol.27 No.1
In order to study the propagation of singularities for solutions to second order quasilinear strictly hyperbolic equations with boundary, we have to consider the regularity of solutions of first order nonlinear equations satisfied by a characteristic hyper-surface. In this paper, we study the regularity compositions of the form v(${\varphi}$(x), x) with v and ${\varphi}$ assumed to have limited Sobolev regularities and we use it to prove the regularity of solutions of the first order nonlinear equations.
THE STABILITY OF THE SOLUTION FOR A HYPERBOLIC PROBLEM ON R^N
Perikles Papadopoulos,Niki Lina Matiadou,Stavros Fatouros 경남대학교 수학교육과 2018 Nonlinear Functional Analysis and Applications Vol.23 No.1
We examine the generalized quasilinear Kirchhoff’s string equation. The purpose of our work is to study the stability of the solution for this equation.
THE ENERGY INEQUALITY OF A QUASILINEAR HYPERBOLIC MIXED PROBLEM
Kang, Seong-Joo Korean Mathematical Society 2001 대한수학회논문집 Vol.16 No.2
In this paper, we establish the energy inequalities for second order quasilinear hyperbolic mixed problems in the domain R_(sup)n.
SOME QUASILINEAR HYPERBOLIC EQUATIONS AND YOSICA APPROXIMATIONS
Park, Jong-Yeoul,Jung, Il-Hyo,Kang, Yong-Han Korean Mathematical Society 2001 대한수학회보 Vol.38 No.3
We show the existence and uniqueness of solutions for the Cauchy problem for nonlinear evolution equations with the strong damping: ${\upsilon}"(t)-M(|{\nablauu}(t)|^2){\triangle}u(t)-{\delta}{\triangle}u'(t)=f(t)$. As an application, a Kirchhoff model with viscosity is given.
Generalized hyperbolic geometric flow
Shahroud Azami,Ghodratallah Fasihi-Ramandi,Vahid Pirhadi 대한수학회 2023 대한수학회논문집 Vol.38 No.2
In the present paper, we consider a kind of generalized hyperbolic geometric flow which has a gradient form. Firstly, we establish the existence and uniqueness for the solution of this flow on an $n$-dimensional closed Riemannian manifold. Then, we give the evolution of some geometric structures of the manifold along this flow.
ENERGY DECAY ESTIMATES FOR A KIRCHHOFF MODEL WITH VISCOSITY
Jung Il-Hyo,Choi Jong-Sool Korean Mathematical Society 2006 대한수학회보 Vol.43 No.2
In this paper we study the uniform decay estimates of the energy for the nonlinear wave equation of Kirchhoff type $$y'(t)-M({\mid}{\nabla}y(t){\mid}^2){\triangle}y(t)\;+\;{\delta}y'(t)=f(t)$$ with the damping constant ${\delta} > 0$ in a bounded domain ${\Omega}\;{\subset}\;\mathbb{R}^n$.