Conditions for the solvability of the Cauchy problem for linear first-order functional differential equations [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2013 Conditions for the unique solvability of the Cauchy problem for a family of scalar functional differential equations are obtained. These conditions are sufficient for the solvability of the Cauchy problem for every equation from the family and are ...
Eugene Bravyi
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On an Approximate Solution of the Cauchy Problem for Systems of Equations of Elliptic Type of the First Order [PDF]
Entropy, 2022 In this paper, on the basis of the Carleman matrix, we explicitly construct a regularized solution of the Cauchy problem for the matrix factorization of Helmholtz’s equation in an unbounded two-dimensional domain.
Davron Aslonqulovich Juraev +2 more
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Cauchy problem for fractional non-autonomous evolution equations [PDF]
Banach Journal of Mathematical Analysis, 2019 This paper deals with the Cauchy problem to a class of nonlinear time fractional non-autonomous integro-differential evolution equation of mixed type via measure of noncompactness in infinite-dimensional Banach spaces.
Pengyu Chen, Xuping Zhang, Yongxiang Li
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The Cauchy Problem for the Fractional Kadomtsev-Petviashvili Equations [PDF]
SIAM Journal on Mathematical Analysis, 2017 The aim of this paper is to prove various ill-posedness and well-posedness results on the Cauchy problem associated to a class of fractional Kadomtsev--Petviashvili (KP) equations, including the KP...
F. Linares, D. Pilod, J. Saut
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Inhomogeneous conformable abstract Cauchy problem
Open Mathematics, 2021 In this paper, we discuss the solution of the inhomogeneous conformable abstract Cauchy problem. The homogeneous problem is also studied. The analysis of conformable fractional calculus and fractional semigroups is also given.
Rabhi Lahcene +2 more
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Localized Method of Fundamental Solutions for Two-Dimensional Inhomogeneous Inverse Cauchy Problems
Mathematics, 2022 Due to the fundamental solutions are employed as basis functions, the localized method of fundamental solution can obtain more accurate numerical results than other localized methods in the homogeneous problems.
Junli Zhang +3 more
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Cauchy problem for the Kuznetsov equation [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2017 We consider the Cauchy problem for a model of non-linear acoustics, named the Kuznetsov equation, describing sound propagation in thermo-viscous elastic media.
A. Dekkers, A. Rozanova-Pierrat
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Blow-up of solutions of Cauchy problem for nonlinear Schrödinger equation
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2013 In this work we study the effect of time finiteness of the existence of Cauchy problem for nonlinear Schrödinger equation solution. Together with the ill-posed Cauchy problem we consider its neighborhood in the space of operators, representing Cauchy ...
Vsevolod Zhanovich Sakbaev
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Global existence and large time asymptotic behavior of strong solutions to the Cauchy problem of 2D density-dependent Navier–Stokes equations with vacuum [PDF]
, 2015 We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier–Stokes equations with vacuum as far-field density.
Boqiang Lü, Xiaoding Shi, X. Zhong
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2016 In the paper the problem of Cauchy is considered for the hyperbolic differential equation of the n-th order with the nonmultiple characteristics. The Cauchy problem is considered for the hyperbolic differential equation of the third order with the ...
Aleksandr A Andreev, Julia O Yakovleva
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