The Cauchy problem

The novelty of the paper is that we have succeeded in deriving the L 1 − L 1 estimates for solutions to (0.1) in general cases of σ > 1 without any constraint condition to space dimensions, i.e. our results are valid for any n ≥ 1.

11p visharma 20-10-2023 3 2   Download

Part 1 of ebook "Proofs from the book" provides readers with contents including: number theory; geometry; six proofs of the infinity of primes; bertrand’s postulate; binomial coefficients are (almost) never powers; representing numbers as sums of two squares; the law of quadratic reciprocity; every finite division ring is a field; hilbert’s third problem - decomposing polyhedra; lines in the plane and decompositions of graphs; the slope problem;...

126p hanlinhchi 29-08-2023 6 2   Download

Continued part 1, part 2 of ebook "Front tracking for hyperbolic conservation laws" provides readers with contents including: Chapter 5 - The riemann problem for systems; Chapter 6 - Existence of solutions of the cauchy problem; Chapter 7 - Well-posedness of the cauchy problem; Chapter 8 - Conservation laws with discontinuous flux functions;...

291p lytamnguyet 04-08-2023 8 4   Download

The author present in the article "The semilinear coupled systems for the external damping models with variable coefficients" some results on the global solvability with arbitrarily small data of the Cauchy problem for the following semilinear coupled system with a variable coefficient.

13p runordie3 27-06-2022 5 2   Download

The paper "Asymptotic of solutions of cauchy - dirichlet problem for hyperbolic equation in infinit cylinders with non - smooth base" is concerned with the asymptotical expansions of generalized solutions of the Cauchy-Dirichlet problem for second order hyperbolic equation in domains with a conical points.

8p thienlangso 15-12-2021 16 1   Download

The main goal of this paper is to obtain the regularity of weak solution of Cauchy-Neumann problem for classical Schrodinger equation in infinite cylinders with the bases containing conical points.

10p larachdumlanat127 20-12-2020 6 0   Download

In this paper, we study the first initial boundary value problem for second-order parabolic equations in cylinders with piecewise smooth base. Some results on the unique existence and on the smoothness with respect to time of the solution are given.

12p tamynhan8 04-11-2020 3 1   Download

In this paper, we study the regularity of the solution for Cauchy-Dirichlet problem for the second order parabolic equations in domains with conical points. The regularity of the solution in Lp-weighted Sobolev spaces will be established.

5p tamynhan8 04-11-2020 13 1   Download

In this article, the considered problem of Cauchy reaction diffusion equation of fractional order is solved by using integral transform of Laplace coupled with decomposition technique due to Adomian scheme. This combination led us to a hybrid method which has been properly used to handle nonlinear and linear problems. The considered problem is used in modeling spatial effects in engineering, biology and ecology. The fractional derivative is considered in Caputo sense. The results are obtained in series form corresponding to the proposed problem of fractional order.

8p dayhoctainha 10-09-2020 18 0   Download

In this paper, we study a Cauchy problem for the heat equation with linear source in the. This problem is ill-posed in the sense of Hadamard. To regularize the problem, the truncation method is proposed to solve the problem in the presence of noisy Cauchy data   and   satisfying We give some error estimates between the regularized solution and the exact solution under some different a-priori conditions of exact solution.

9p gildur 30-11-2019 11 1   Download

oblem for a ND nonlinear elliptic equation in a bounded domain. As we know, the problem is severely ill-posed. We apply the Fourier truncation method to regularize the problem. Error estimates between the regularized solution and the exact solution are established in p H space under some priori assumptions on the exact solution.

10p gildur 30-11-2019 8 1   Download

In this report, we examine the unsteady Stokes equations with nonhomogeneous boundary conditions. As an application of a Carleman estimate, we first establish log type stabilities for the solution of the equations from either an interior measurement of the velocity, or a boundary observation depending on the trace of the velocity and of the Cauchy stress tensor measurements on a part of the boundary.

16p viartemis2711 22-10-2019 11 1   Download

This paper’s purpose is to investigate the BHP on a disk, especially, the problem is associated with the perturbed diffusivity and the space-dependent heat source. In order to solve the problem, the authors apply the separation of variables method, associated with the Bessel’s equation and Bessel’s expansion.

18p vicross2711 20-06-2019 14 0   Download

We construct an iteration sequence converging (in the uniform norm in the space of continuous functions) to the solution of the Cauchy problem for a singularly perturbed weakly nonlinear differential equation of an arbitrary order (the weak nonlinearity means the presence of a small parameter in the nonlinear term).

13p nutifooddau 21-01-2019 22 1   Download

We consider the existence, both locally and globally in time, the global nonexistence, and the asymptotic behavior of solutions for the Cauchy problem of a multidimensional generalized Boussinesq-type equation with a damping term.

22p danhdanh27 07-01-2019 22 2   Download

The parabolic equation is of divergence form with discontinuous coefficients. We consider a nonlinear condition on a part of the boundary such that the power laws (and the Robin boundary condition) appear as particular cases.

18p danhdanh27 07-01-2019 11 1   Download

We consider an inverse problem for determining an inhomogeneity in a viscoelastic body of the Zener type, using Cauchy boundary data, under cyclic loads at low frequency. We show that the inverse problem reduces to the one for the Helmholtz equation and to the same nonlinear Calderon equation given for the harmonic case. A method of solution is proposed which consists in two steps : solution of a source inverse problem, then solution of a linear Volterra integral equation.

9p thienthanquydu 23-10-2018 27 0   Download

Thus the aim is to determine the solution of a known PDE defined throughout the domain, which satisfies the superabundant data and then identifies the missing ones. For linear symmetric operators, we propose a general method to solve the data completion problem as a Cauchy problem. Various applications are described for stationary conduction and elastostatic problems.

15p thienthanquydu 23-10-2018 30 1   Download

Let rl be a bounded domain in the plane, representing an elastic body. Let ro be a portion of the boundary r of rl, ro being assumed to be parallcd to the x - axis. It is proposed to determine the stress field in n from the displacements and surface stresses given on r 0 . Under the assumption of plane stress, it is shown that ux + uy is a harmonic function. An Airy stress function is introduced, from which the stress field is computed.

4p thienthanquydu 21-10-2018 30 1   Download

Contructive Problems, Binary and other base, Constructing functions by iterations, Approximating with linear functions, Extremal element method, Multiplicative Cauchy Equation, As the main contents of the document "Functional Equations: Electronic Edition 2007". Each of your content and references for additional lectures will serve the needs of learning and research.

143p daicatho1989 25-01-2016 43 5   Download