Existence and Uniqueness of Solutions to Semilinear Nonlocal Parabolic Equations
نویسندگان
چکیده
منابع مشابه
Existence of Mild Solutions for Nonlocal Semilinear Fractional Evolution Equations
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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= −divax, t∇u + b⃗x, t ⋅ ∇u + cx, tux, t with aij, bj, c ∈ LUT and for a0 > 0, z⃗ ⋅ aijx, t z⃗ ≥ a0 | z⃗| ∀z⃗ ∀x, t ∈ UT. Then L is said to be uniformly elliptic on UT. We recall that the assumptions on the coefficients aij, bj, c, imply the existence of positive constants, a1,a0 and μ0 such that for all u,v ∈ H1U, and μ > μ0, |Bu,v, t| ≤ a1‖u‖1‖v‖1 a.e. t ∈ 0,T Bu,u, t +...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1993
ISSN: 0022-247X
DOI: 10.1006/jmaa.1993.1022