Mild solutions of semilinear evolution equation and their applications in second‐order hyperbolic PDE
نویسندگان
چکیده
The principal goal of this work is to solvability the mild solution for second‐order hyperbolic PDE with initial/boundary‐value problem nonlocal condition form where open. Our analysis relies on technique measure noncompactness.
منابع مشابه
Existence of mild solutions for semilinear equation of evolution
Abstract. The aim of this paper is to give an existence theorem for a semilinear equation of evolution in the case when the generator of semigroup of operators depends on time parameter. The paper is a generalization of [2]. Basing on the notion of a measure of noncompactness in Banach space, we prove the existence of mild solutions of the equation considered. Additionally, the applicability of...
متن کاملGeneralized Solutions to Semilinear Elliptic Pde with Applications to the Lichnerowicz Equation
In this article we investigate the existence of a solution to a semi-linear, elliptic, partial differential equation with distributional coefficients and data. The problem we consider is a generalization of the Lichnerowicz equation that one encounters in studying the constraint equations in general relativity. Our method for solving this problem consists of solving a net of regularized, semi-l...
متن کاملExistence 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 ...
متن کاملBounded Solutions of Second Order Semilinear Evolution Equations and Applications to the Telegraph Equation
Motivated by the problem of the existence of a solution of the nonlinear telegraph equation wt + clll u,, + h(t. c, u) = 0, such that u(t, ,) satisfies suitable boundary conditions over (0,~) ar;d Ilu(t,.)II is bounded over W for some function space norm 11 11: we prove the existence of bounded solutions over R of semilinear evolution equations in a Hilbert space of the form ii + cti + Au + g(t...
متن کاملExact controllability of semilinear evolution equation and applications
where Z, U are Hilbert spaces, A : D(A) ⊂ Z −→ Z is the infinitesimal generator of strongly continuous semigroup {T (t)}t≥0 inZ, B ∈ L(U,Z), the control function u belongs to L(0, τ ;U) and F : [0, τ ]× Z × U −→ Z is a suitable function. First, we give a necessary and sufficient condition for the exact controllability of the linear system z′ = Az + Bu(t); Second, under some conditions on F , we...
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: Mathematical Methods in The Applied Sciences
سال: 2023
ISSN: ['1099-1476', '0170-4214']
DOI: https://doi.org/10.1002/mma.9148