Particle Dynamics Subject to Impenetrable Boundaries: Existence and Uniqueness of Mild Solutions
نویسندگان
چکیده
منابع مشابه
Existence and uniqueness of mild solutions to initial value problems for fractional evolution equations
For more details as regards semigroup theory of operators, see [1]. Fractional differential equations have been widely applied in many important areas, including thermodynamics, porous media, plasma dynamics, cosmic rays, continuum mechanics, electrodynamics, quantummechanics, biological systems and prime number theory [2, 3]. In particular, the fractional diffusion equations have been successf...
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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: SIAM Journal on Mathematical Analysis
سال: 2019
ISSN: 0036-1410,1095-7154
DOI: 10.1137/18m1235922