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The Algebro-Geometric Initial Value Problem for the Ruijsenaars-Toda Hierarchy and Quasi-Periodic Solutions
Ruijsenaars-Toda hierarchy complex-valued algebro-geometric solutions hyperelliptic curve Dubrovin-type equation Baker-Akhiezer vector
2012/4/27
We provide a detailed treatment of Ruijsenaars-Toda (RT) hierarchy with special emphasis on its the theta function representation of all algebro-geometric solutions. The basic tools involve hyperellip...
Initial-boundary value problem for the equation of timelike extremal surfaces in Minkowski space
Applied mathematics Minkowski space Timelike extremal surfaces Initial-boundary value problem
2011/10/15
In this paper we investigate the mixed initial-boundary value problem for the equation of time-like extremal surfaces in Minkowski space $R^{1+(1+n)}$ in the first quadrant. Under the assumptions that...
On the Local Existence for the Characteristic Initial Value Problem in General Relativity
Characteristic Initial Value Problem General Relativity Analysis of PDEs
2011/9/29
Abstract: Given a truncated incoming null cone and a truncated outgoing null cone intersecting at a two sphere $S$ with smooth characteristic initial data, a theorem of Rendall shows that the vacuum E...
Boundary value problem for a classical semilinear parabolic equation
positive solution global existence blow-up omega-limit
2011/2/28
In this paper, we study the boundary value problem of the classical semilinear parabolic equations ut − u = |u|p−1u.
Initial-boundary value problems for second order systems of partial differential equations
Initial-boundary value problems second order systems of partial differential equations
2011/1/18
We develop a well-posedness theory for second order systems in bounded domains where
boundary phenomena like glancing and surface waves play an important role. Attempts have previ-
ously been made t...
Well-posedness of a Class of Non-homogeneous Boundary Value Problems of the Korteweg-de Vries Equation on a Finite Domain
Class of Non-homogeneous Boundary Value Problems Korteweg-de Vries Equation Finite Domain
2011/1/18
In this paper, we study a class of initial and boundary value problems proposed by Colin and Ghidalia for the Korteweg-de Vries equation posed on a bounded domain (0, L).We show that the initial-value...
Lie symmetries of nonlinear boundary value problems
Lie symmetries nonlinear boundary value problems
2011/2/28
Nonlinear boundary value problems (BVPs) by means of the classical Lie symmetry method are studied. A new definition of Lie invariance for BVPs are proposed by the gen-eralization of existing those on...
A PDE approach to large-time asymptotics for boundary-value problems for nonconvex Hamilton-Jacobi Equations
Large-time Behavior Hamilton-Jacobi Equations Initial-Boundary Value Problem
2011/1/18
We investigate the large-time behavior of three types of initial-boundary value problems for Hamilton-Jacobi Equations with nonconvex Hamiltonians.