منابع مشابه
Generalized Solutions of a Periodic Goursat Problem
Under reasonable assumptions on the data u, v and the function f , we show that the nonlinear periodic Goursat problem ∂u ∂x∂y (x, y) = f(x, y, u(x, y)); u(x, 0) = v(x); u(0, y) = w(y) which cannot be posed in the general theory of distributions, may be studied and solved in a differential algebra of periodic new generalized functions on R2. This algebra contains, in a canonical way, the space ...
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We consider the quasilinear Kirchhoff's problem$$ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+f(u)=0 ,;; x in {mathcal{R}}^{N}, ;; t geq 0,$$with the initial conditions $ u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ; f(u)=|u|^{a}u$ and $(phi (x))^{-1} in L^{N/2}({mathcal{R}}^{N})cap L^{infty}({mathcal{R}}^{N} )$ is a positive function. The purpose of our work is to ...
متن کاملon the goursat problem for a linear partial differential equation
in this paper, the goursat problem of a general form for a linear partial differential equation is investigated with the help of the riemann function method. some results are given concerning the existence and uniqueness for the solution of the suggested problem.
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In the paper, the bang-bang principle for a control system connected with a system of linear nonautonomous partial differential equations of hyperbolic type (the socalled Goursat-Darboux problem or continuous Fornasini-Marchesini problem) is proved. Some density result is also obtained.
متن کاملThe upper Lyapunov exponent of S1(2,R) cocycles: Discontinuity and the problem of positivity
Let T be an aperiodic automorphism of a standard probability space (X,m). Let V be the subset of A = L°°(X% 5/(2, R)) where the upper Lyapunov exponent is positive almost everywhere. We prove that the set V \ int(V) is not empty. So, there are always points in A where the Lyapunov exponents are discontinuous. We show further that the decision whether a given cocycle is in V is at least as hard ...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1989
ISSN: 0022-1236
DOI: 10.1016/0022-1236(89)90025-6