Hyperbolic equation with singular coefficient
نویسندگان
چکیده
منابع مشابه
A Linear First-order Hyperbolic Equation with a Discontinuous Coefficient: Distributional Shadows and Propagation of Singularities
It is well-known that distributional solutions to the Cauchy problem for ut +(b(t, x)u)x = 0 with b(t, x) = 2H(x− t), where H is the Heaviside function, are non-unique. However, it has a unique generalized solution in the sense of Colombeau. The relationship between its generalized solutions and distributional solutions is established. Moreover, the propagation of singularities is studied.
متن کاملA Collocation-Galerkin Method for a First Order Hyperbolic Equation With Space and Time-Dependent Coefficient
A collocation-Galerkin scheme is proposed for an initial-boundary value problem for a first order hyperbolic equation in one space dimension. The Galerkin equations satisfied by the approximating solution are obtained from a weak-weak formulation of the initial-boundary value problem. The collocation points are taken to be affine images of the roots of the Jacobian polynomials of degree r — \ o...
متن کاملPositive periodic solution for higher-order p-Laplacian neutral singular Rayleigh equation with variable coefficient
where p > , φp(x) = |x|p–x for x = and φp() = , c ∈ Cn(R,R) and c(t + T) ≡ c(t), f is a continuous function defined in R and periodic in t with f (t, ·) = f (t + T , ·) and f (t, ) = , g(t,x) = g(x) + g(t,x), where g : R × (, +∞) → R is an L-Carathéodory function, g(t, ·) = g(t + T , ·), g ∈ C((,∞);R) has a singularity at x = , e : R→ R is a continuous periodic function with ...
متن کاملOn a Class of Singular Hyperbolic Equation with a Weighted Integral Condition
In this paper, we study a mixed problem with a nonlocal condition for a class of second order singular hyperbolic equations. We prove the existence and uniqueness of a strong solution. The proof is based on a priori estimate and on the density of the range of the operator generated by the studied problem.
متن کاملOn Hill’s Equation with a Discontinuous Coefficient
where q(x) and r(x) are real valued and all have period a. Also q(x) is piecewise continuous, r ′′(x) is piecewise continuous in (0,b) and (b,a) where 0< b < a and r(x)≥ r0 (> 0). Those values of complex parameter λ, for which periodic or antiperiodic problem associated with (1.1) and the x-interval (0,a) has a nontrivial solution y(x,λ), are called eigenvalues. An equation giving the eigenvalu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Researches in Mathematics and Mechanics
سال: 2017
ISSN: 2519-206X
DOI: 10.18524/2519-206x.2017.1(29).135733