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On a final value problem for a nonhomogeneous fractional pseudo-parabolic equation
Alexandria Engineering Journal, 2020 In this paper, we are interested in finding the function u(t,x),(t,x)∈[0,T)×Ω from the final data u(T,x)=ϕ(x), satisfies a nonhomogeneous fractional pseudo-parabolic equation. The problem is stable for the cases σν, the problem is ill-posed (in the sense
Nguyen Hoang Luc +3 more
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Final Value Problem for Parabolic Equation with Fractional Laplacian and Kirchhoff’s Term [PDF]
Journal of Function Spaces, 2021 In this paper, we study a diffusion equation of the Kirchhoff type with a conformable fractional derivative. The global existence and uniqueness of mild solutions are established. Some regularity results for the mild solution are also derived.
Nguyen Hoang Luc +3 more
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A Class of Well-Posed Parabolic Final Value Problems [PDF]
, 2020 This paper focuses on parabolic final value problems, and well-posedness is proved for a large class of these. The clarification is obtained from Hilbert spaces that characterise data that give existence, uniqueness and stability of the solutions.
Jon Johnsen
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Final Value Problems for Parabolic Differential Equations and Their Well-Posedness [PDF]
Axioms, 2018 This article concerns the basic understanding of parabolic final value problems, and a large class of such problems is proved to be well posed. The clarification is obtained via explicit Hilbert spaces that characterise the possible data, giving ...
Ann-Eva Christensen, Jon Johnsen
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Final-value problem for a weakly-coupled system of structurally damped waves
Electronic Journal of Differential Equations, 2018 We consider the final-value problem of a system of strongly-damped wave equations. First of all, we find a solution of the system, then by an example we show the problem is ill-posed.
Nguyen Huy Tuan +3 more
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The Final Value Problem for Sobolev Equations [PDF]
Proceedings of the American Mathematical Society, 1976 Let A A and B B be m m -accretive linear operators in a complex Hilbert space H H with D ( A ) ⊂ D ( B ) D(A) \subset D(B) .
John E. Lagnese
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On parabolic final value problems and well-posedness [PDF]
Comptes Rendus. Mathématique, 2018 We prove that a large class of parabolic final value problems is well posed. This results via explicit Hilbert spaces that characterise the data yielding existence, uniqueness and stability of solutions. This data space is the graph normed domain of an unbounded operator, which represents a new compatibility condition pertinent for final value problems.
Ann-Eva Christensen, Jon Johnsen
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The Definition and Numerical Method of Final Value Problem and Arbitrary Value Problem [PDF]
Computer Systems Science and Engineering, 2018 Scheduled for publication in the September 2018 edition of CSSE(Computer Systems Science and Engineering) journal, Volume 33 Number ...
Shixiong Wang +3 more
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Optimal Dynamic Portfolio with Mean-CVaR Criterion [PDF]
Risks, 2013 Value-at-risk (VaR) and conditional value-at-risk (CVaR) are popular risk measures from academic, industrial and regulatory perspectives. The problem of minimizing CVaR is theoretically known to be of a Neyman–Pearson type binary solution.
Mingxin Xu, Jing Li
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Initial-final value problems for ordinary differential equations and applicatlons to equivariant harmonic maps [PDF]
Journal of the Mathematical Society of Japan, 1998 The following ordinary differential equation \[ \ddot r(t)+ \Biggl\{p{\dot f_1(t)\over f_1(t)}+ q{\dot f_2(t)\over f_2(t)}\Biggr\}\dot r(t)- \Biggl\{\mu^2 {h_1(r(t)) h_1'(r(t))\over f_1(t)^2}+ \nu^2{h_2(r(t)) h_2'(r(t))\over f_2(t)^2}\Biggr\}= 0,\;(0,\infty) \] with \(\lim_{t\to 0}(r(t))= 0\), where \(f_i\) and \(h_i\) are given functions defined on \((
Takeyuki Nagasawa, Keisuke Ueno
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