Showing papers in "Japan Journal of Applied Mathematics in 1986"
TL;DR: In this paper, the asymptotic behavior toward the rarefaction waves of the solution of a one-dimensional model system associated with compressible viscous gas is studied.
Abstract: This paper is concerned with the asymptotic behavior toward the rarefaction waves of the solution of a one-dimensional model system associated with compressible viscous gas If the initial data are suitably close to a constant state and their asymptotic values atx=±∞ are chosen so that the Riemann problem for the corresponding hyperbolic system admits the weak rarefaction waves, then the solution is proved to tend toward the rarefaction waves ast→+∞ The proof is given by an elementaryL
2 energy method
287 citations
TL;DR: In this article, the Cauchy problem for the compressible Euler equation with compactly supported initials is discussed and a new symmetrization for initials having compact support or vanishing at infinity is introduced.
Abstract: The Cauchy problem for the compressible Euler equation is discussed with compactly supported initials To establish the localexistence of classical solutions by the aid of the theory of quasilinear symmetric hyperbolic systems, a new symmetrization is introduced which works for initials having compact support or vanishing at infinity It is further shown that as far as the classical solution is concerned, its support does not change, and that the life span is finite for any solution except for the trivial zero solution
206 citations
TL;DR: In this paper, a convergence theorem for Newton's method in Banach spaces is given, which improves the theorems of Kantorovich [4], Lancaster [8] and Ostrowski [10].
Abstract: On the basis of the results obtained in a series of papers [25]–[28], a convergence theorem for Newton’s method in Banach spaces is given, which improves the theorems of Kantorovich [4], Lancaster [8] and Ostrowski [10]. The error bounds obtained improve the recent results of Potra [17].
110 citations
TL;DR: In this paper, a self-affine function whose typical example is the component function of the famous Peano curve (P1(t),P2(t)), 0≤t≤1.
Abstract: We define a self-affine function whose typical example is the component function of the famous Peano curve (P1(t),P2(t)), 0≤t≤1. We obtain the Hausdorff and packing dimension of the graph of a self-affine function under some conditions. We also prove that the functionP1(t−P2(t) has a continuous occupation density with respect to time and space which will be the first example of a continuous deterministic function whose occupation density is continuous with respect to time and space.
60 citations
TL;DR: In this paper, the existence and stability of monotone traveling wave solutions for nonlinear parabolic equations arising in population dynamics was shown and the asymptotic behavior of solutions of the pure initial value problem was investigated.
Abstract: In this paper, we show the existence and stability of monotone traveling wave solutions for some nonlinear parabolic equations arising in population dynamics. Using these traveling wave solutions as comparison functions, we investigate the asymptotic behavior of solutions of the pure initial value problem and estimate the support of the solutions.
37 citations
TL;DR: It follows from them that there exist exactly a countably infinite number of self-affine functions modulo constant multiplications.
Abstract: A characterization of self-affine functions as functions generated by finite automata is given. Also, a kind of uniqueness in representing a self-affine function by a finite automaton is proved. It follows from them that there exist exactly a countably infinite number of self-affine functions modulo constant multiplications.
34 citations
TL;DR: The entropy functional of an input source and the mutual entropy functional for a Gaussian channel are introduced and a fundamental inequality for communication processes is shown.
Abstract: In order to discuss communication processes consistently for a Gaussian input with a Gaussian channel on an infinite dimensional Hilbert space, we introduce the entropy functional of an input source and the mutual entropy functional for a Gaussian channel and show a fundamental inequality for communication processes.
28 citations
TL;DR: In this article, the authors considered a three-particle system with nearest neighbor interaction and showed that under a condition which is generically fulfilled all periodic solutions near a normal mode frequency are obtained and their symmetry properties are investigated.
Abstract: We consider a circular chain ofN particles with nearest neighbour interaction. Under a condition which is generically fulfilled all periodic solutions near a normal mode frequency are obtained and their symmetry properties are investigated. The genericity condition is explicitly evaluated for a three particle system.
24 citations
TL;DR: In this article, a method for deriving newa posteriori error bounds for Newton-like methods in a Banach space under Kantorovich type assumptions is presented, which are sharper than those of Miel [10] and include those recently obtained by Moret [12].
Abstract: This paper provides a method for deriving newa posteriori error bounds for Newton-like methods in a Banach space under Kantorovich type assumptions. The bounds found are sharper than those of Miel [10] and include those recently obtained by Moret [12]. The applicability of our method is studied for other types of iterations including Newton’s method.
15 citations
TL;DR: In this paper, the authors studied the asymptotic behavior of weak solutions to a multi-phase Stefan problem for a quasi-linear heat equation of the form ρ(v) t - Δv=ƒ in several space variables, with Dirichlet-Neumann boundary condition on the fixed boundary.
Abstract: This paper is concerned with the asymptotic behavior of weak solutions to a multi-phase Stefan problem for a quasi-linear heat equation of the form ρ(v) t - Δv=ƒ in several space variables, with Dirichlet-Neumann boundary condition on the fixed boundary. We shall discuss the asymptotic convergence of the enthalpy and temperature inL 2(Ω) andH 1(Ω), respectively, when the prescribed boundary data asymptotically converge in some sense. Our approach to the investigation of the asymptotic convergence of solutions is based on the theory of nonlinear evolution equations governed by time-dependent subdifferential operators in Hilbert spaces. The results obtained in this paper improve on those established so far.
14 citations
TL;DR: In this article, it was shown that V(Ω) is isomorphic to H1(ε)3 ∩V(δ) when Ω is convex, where H 1 is the usual first order Sobolev space.
Abstract: Let Ω be a bounded domain inR3 with Lipschitz continuous boundary ∂Ω. In electromagnetism, we use the Hilbert spaceV(Ω) of vector-valued functions which, along with their rotations and divergences, are square summable in Ω and whose tangential components on ∂Ω vanish. In this paper, it is proven thatV(Ω) is isomorphic to {H1(Ω)}3 ∩V(Ω) when Ω is convex, whereH1(Ω) is the usual first order Sobolev space. To this end, we adopt the techniques given by Grisvard and the mixed formulation.
TL;DR: In this paper, the authors generalize the definition of exponential dichotomy and give another simple proof of Urabe's Existence Theorem to nonlinear quasiperiodic differential equations.
Abstract: The paper first generalizes the definition of exponential dichotomy and gives another simple proof of Urabe’s Existence Theorem to nonlinear quasiperiodic differential equations. Next, a useful numerical analysis of quasiperiodic solutions to second order differential equations is presented. The paper extends the results given in previous papers [3], [9], [16] which dealt with weakly nonlinear differential equations. A few examples of numerical analysis of Van der Pol type equations are illustrated.
TL;DR: In this paper, a spatially aggregating population model governed by a nonlinear degenerate diffusion and advection equation is considered, where the interface implies the time-dependent boundary between the populated region and the unpopulated one.
Abstract: We consider a spatially aggregating population model which is governed by a nonlinear degenerate diffusion and advection equation. The interface in this model implies the time-dependent boundary between the populated region and the unpopulated one. The asymptotic behavior of the interface is almost completely investigated.
TL;DR: A generalized doubly stochastic (g.d.s.) matrix is an ann×n matrix such that each row and each column sum is equal to a givenx≠0 in a fieldF as mentioned in this paper.
Abstract: A generalized doubly stochastic (g.d.s.) matrix is ann×n matrix such that each row and each column sum is equal to a givenx≠0 in a fieldF. The setA
n
of all such g.d.s. matrices is investigated in this paper. The addition ⊕, scalar multiplication ° and product ⊕ inA
n
are defined so thatA
n
becomes a simple algebra of dimension (n−1)2. The subsetW
n
of then-dimensional vector spaceV
n
of all vectors with coordinate sum equal tox is defined to be a linear space under ⊕ and °. It is proven that (A
n
, ⊕, °, ⊕) is the total algebra of linear operators on (W
n
, ⊕, °). Equivalance and similarity of g.d.s. matrices inA
n
is also investigated. A basis of (n−1)2 permutation matrices inA
n
is constructed so that eachA ∈A
n
can be represented as a linear combination of these matrices.
TL;DR: In this paper, a retarded functional differential equation (also an ordinary differential equation) representing weakly coupled oscillators is considered, and it is shown that the solution surface constructed by such branches is projected onto the Klein bottle.
Abstract: A retarded functional differential equation (also an ordinary differential equation) representing weakly coupled oscillators is considered. This equation with two parameters has a singularity, for certain parameter values, such that the linearized equation around a steady state has a pair of conjugate pure imaginary eigenvalues of double multiplicity. Solving the bifurcation equations for periodic solutions around the singularity, it is shown that there exists a secondary bifurcating branch which connects two kinds of primary bifurcating periodic solutions. Furthermore if the coupling terms is varied suitably, striking deformation of this branch is observed. Namely, the solution surface constructed by such branches is projected onto the Klein Bottle.
TL;DR: In this paper, an iterative algorithm was proposed to calculate the Floquet-Liapounov exponents of the linear differential equation with periodic coefficients (nth order Hill's equation).
Abstract: We present an iterative algorithm which makes it possible to calculate the Floquet-Liapounov exponents of the linear differential equation with periodic coefficients (nth order Hill’s equation). This algorithm is easy to apply and converges rapidly. It is found on a generalization of Hill’s work and on the construction, from a truncature of the infinite determinant, of a contracting mapping which makes it possible to control error.
TL;DR: In this article, the Ritz method for strong elliptic pseudo-differential equations is discussed and the optimal local error estimates are derived if the underlying approximation spaces are finite elements.
Abstract: The Ritz method for strong elliptic pseudo-differential equations is discussed ‘Optimal’ local error estimates are derived if the underlying ‘approximation-spaces’ are finite elements The analysis covers simultaneously pseudo-differential operators of positive and negative order In case of positive order an additional regularity assumption for the ‘approximation-spaces’ is needed
TL;DR: In this paper, an iterative method to solve a system of nonlinear equations arising from finite element analysis of plasticity is proposed, and it is proved that this iteration converges unconditionally.
Abstract: An iterative method to solve a system of nonlinear equations arising from finite element analysis of plasticity is proposed. It is proved that this iteration converges unconditionally. A method to accelerate the convergence of this iteration is also proposed.
TL;DR: This work studies the convergence of a sampler process constructed by the methods stated in Introduction and applies convergence theorems to the restoration of degraded images in image processing.
Abstract: We consider sampling methods for multidimensional random fields. We study the convergence of a sampler process constructed by the methods stated in Introduction. We can apply convergence theorems to the restoration of degraded images in image processing.
TL;DR: In this paper, an approach to dynamic finite two-player games is presented, where some results related to the minimax theorem in a dynamic way are presented, and an approach for dynamic finite games is considered.
Abstract: This paper considers an approach to dynamic finite two person games. Some results related to the minimax theorem in a dynamic way are presented.
TL;DR: In this paper, the location of the nearest singularity from the origin is given by the radiusR of convergence of a power series and the value ofR is calculated numerically by the formula of Cauchy-Hadamard and by that of d'Alembert.
Abstract: The solutions for the Painleve-I equation are expected to be new transcendental functions. But we do not have any concrete information about each solution. The simplest power series solution which is regular at the origin is considered. One of the most important features of this solution is the location of singularities. The location of the nearest singularity from the origin is given by the radiusR of convergence of this power series. The value ofR is calculated numerically by the formula of Cauchy-Hadamard and by that of d’Alembert. A theoretically correct method calculatingR is proposed. We derive some Briot-Bouquet equation from the Painleve-I equation and solve it numerically by the Runge-Kutta method. Thus we obtainedR=2.6155…. Accurate theoretical bounds forR are also obtained by various methods.
TL;DR: In this article, the feasibility and periodicity of the knapsack problem for equality-constraint integer linear programs with mixed signs in the constraint coefficients is investigated. But the complexity of the main part does not depend on the number of variables involved, provided that the constraints are bounded.
Abstract: Two sets of numbers are generated to determine the feasibility and periodicity for an equality-constraint knapsack problem. By aid of the two sets, it is shown that for only a finite number of right hand side numbers the knapsack problem is hard. A novel method is given for solving such hard knapsack problems, of which the complexities of a main part does not depend on the number of variables involved, provided that the constraint coefficients are bounded. A method for representing all the optimal solutions of the knapsack problem for all right hand side numbers is further shown. A similar theory is also developed for an equality-constraint integer linear program with mixed signs in the constraint coefficients.