ON APPROXIMATE SOLUTIONS OF SEMILINEAR EVOLUTION EQUATIONS
نویسندگان
چکیده
منابع مشابه
On approximate solutions of semilinear evolution equations
A general framework is presented to discuss the approximate solutions of an evolution equation in a Banach space, with a linear part generating a semigroup and a sufficiently smooth nonlinear part. A theorem is presented, allowing to infer from an approximate solution the existence of an exact solution. According to this theorem, the interval of existence of the exact solution and the distance ...
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In our previous paper [12], a general framework was outlined to treat the approximate solutions of semilinear evolution equations; more precisely, a scheme was presented to infer from an approximate solution the existence (local or global in time) of an exact solution, and to estimate their distance. In the first half of the present work the abstract framework of [12] is extended, so as to be a...
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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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For a fixed p and σ > −1, such that p > max{1, σ + 1}, one main concern of this paper is to find sufficient conditions for non solvability of ut = −(−∆) β 2 u− V (x)u+ th(x)u +W (x, t), posed in ST := R × (0, T ), where 0 < T < +∞, (−∆) β 2 with 0 < β ≤ 2 is the β/2 fractional power of the −∆, and W (x, t) = tw(x) ≥ 0. The potential V satisfies lim sup|x|→+∞ |V (x)||x| < +∞, for some positive a...
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ژورنال
عنوان ژورنال: Reviews in Mathematical Physics
سال: 2004
ISSN: 0129-055X,1793-6659
DOI: 10.1142/s0129055x04002023