Showing papers in "Journal of Differential Equations in 1975"

TL;DR: In this article, the authors considered the Riemann problem for general n-conservation laws and proved uniqueness and existence theorems subject to condition (E), which is equivalent to Lax's shock inequalities when the system is "genuinely nonlinear".

TL;DR: In this article, a nonlinear autonomous parabolic partial differential equation in one space variable subject to Neumann boundary conditions on a compact interval is investigated and conditions under which a solution has a nonempty ω-limit set.

TL;DR: In this article, the authors used control-theoretic methods to establish, in certain cases, explicit nonuniform decay rates for damped linear oscillators in Hilbert space X: x + B x + Ax = 0, A > 0, B ⩾ 0.

TL;DR: In this article, projection methods based on expansions of solutions of retarded function differential equations in terms of generalized eigenfunctions are considered, and convergence results are established for a class of perturbed systems.

TL;DR: In this paper, the authors specialize some of the results of Delfour and Mitter (J. Differential Equations, 12, 1972, 213-235) to a class of representable affine hereditary differential systems, and introduce the hereditary adjoint system, and give an integral representation of solutions.

TL;DR: In this article, a family of C vector fields on a connected manifold M of dimension n, and B functions on the real line with values in Ri.t functions are considered.

TL;DR: In this paper, an existence theorem coupled with necessary conditions for the relaxed problem of the optimal control of ordinary differential equations in which the cost functional, the restrictions, and the right hand sides are Lipschitz-continuous (but not necessarily differentiable) in their dependence on the state variables is derived.

TL;DR: In this article, the authors considered the solvability of the boundary value problem for partial differential equations, where A is a continuous self-adjoint operator defined on a real Hilbert space H with values in H, the null-space of A is nontrivial, and N is a nonlinear completely continuous perturbation.

TL;DR: In this paper, a new approach was taken in studying the asymptotic behavior of solutions of Eq. (1) by examining the quotient r(t)/q(t) as t + 03, without requiring that the forcing term, Y(Z), be small.

TL;DR: In this paper, the quasilinear, parabolic boundary value problem is treated and sufficient conditions on the functions ǫ(x, t, u, u) for this problem to have a periodic solution u ( x, t ) which may be constructed by successive approximations with an integral operator.

TL;DR: In this paper, it was shown that the lowest eigenvalue of one of the two spectra can be omitted without affecting the conclusions of the results of the other, and that the difference of two such q's correspond to two such problems with the same problem.

TL;DR: In this article, an explicit expression for the reachable set for a class of nonlinear systems was obtained by a chain condition on the Lie algebra of vector fields associated with each nonlinear system, which is used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.

TL;DR: In this article, the authors make the following assumptions: (0.3) a.e. in J2 with some constant C, > 0, and a.m. in 52, u&e) EL-q-l).

TL;DR: In this article, a sufficient condition is derived that one system locally approximates the other, i.e., there exists a map between the state spaces which carries the trajectory of the first system for any control into the trajectory for the same control with an error that grows like a power of t.

TL;DR: In this paper, the lplth order differential equation with perturbed arguments is studied and the results of the same nature with Theorem 1 in [2] concerning the unforced case cannot be included in it.