On existence and uniqueness of solutions for semilinear fractional wave equations
نویسندگان
چکیده
منابع مشابه
On Existence and Uniqueness of Solutions for Semilinear Fractional Wave Equations
Let Ω be a C2-bounded domain of Rd, d = 2, 3, and fix Q = (0, T )×Ω with T ∈ (0,+∞]. In the present paper we consider a Dirichlet initial-boundary value problem associated to the semilinear fractional wave equation ∂α t u + Au = fb(u) in Q where 1 < α < 2, ∂α t corresponds to the Caputo fractional derivative of order α, A is an elliptic operator and the nonlinearity fb ∈ C1(R) satisfies fb(0) =...
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In this paper, we investigate a class of semilinear fractional evolution equations with nonlocal initial conditions given by (1) ⎧⎨ ⎩ dqu(t) dtq = Au(t)+(Fu)(t), t ∈ I, u(0)+g(u) = u0, where 0 < q< 1 , I is a compact interval. Sufficient conditions for the existence of mild solutions for the equation (1) are derived. The main tools include Laplace transform, Arzela-Ascoli’s Theorem, Schauder’s ...
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In this work we prove a result concernig the existence and uniqueness of solutions of quasilinear wave equation and we consider also their trivial solutions. We consider the following initial-boundary value problem for the nonlinear wave equation in the form u+ f (u) + g (u̇) = 0 in [0, T ) × Ω (QL) with initial values u0 = u (0, ·) , u1 = u̇ (0, ·) and boundary vale null, that is, u (t, x) = 0 o...
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ژورنال
عنوان ژورنال: Fractional Calculus and Applied Analysis
سال: 2017
ISSN: 1311-0454,1314-2224
DOI: 10.1515/fca-2017-0006