相关论文: A Method of the Study of the Cauchy Problem for a …

We consider an elliptic self-adjoint first order pseudodifferential operator acting on columns of complex-valued half-densities over a connected compact manifold without boundary. The eigenvalues of the principal symbol are assumed to be…

We present a general method for studying long time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations,…

We deal with the Cauchy problem for multi-dimensional scalar conservation laws, where the fluxes and the source terms can be discontinuous functions of the unknown. The main novelty of the paper is the introduction of a~kinetic formulation…

In this paper we study the asymptotic behavior of solutions to systems of strongly coupled integral equations with oscillatory coefficients. The system of equations is motivated by a peridynamic model of the deformation of heterogeneous…

The Cauchy problem for the inhomogeneous Helmholtz equation with non-uniform refraction index is considered. The ill-posedness of this problem is tackled by means of the variational form of mollification. This approach is proved to be…

We develop a new method of constructing a large N asymptotic series in powers of $N^{-1/2}$ for the function of N arguments which is a solution to the Cauchy problem for the equation of a special type. Many-particle Wigner, Schr\"{o}dinger…

In this paper we give stochastic solutions of conformable fractional Cauchy problems. The stochastic solutions are obtained by running the processes corresponding to Cauchy problems with a nonlinear deterministic clock.

Given a sequence of Cauchy-distributed random variables defined by a sequence of location parameters and a sequence of scale parameters, we consider another sequence of random variables that is obtained by perturbing the location or scale…

We quantify the uniqueness of continuation from Cauchy or interior data. Our approach consists in extending the existing results in the linear case. As by product we obtain a new stability estimate in the linear case. We also show the…

We study the Cauchy problem for the defocusing nonlinear Schr\"odinger (NLS) equation under the assumption that the solution vanishes as $x \to + \infty$ and approaches an oscillatory plane wave as $x \to -\infty$. We first develop an…

We find a representation of smooth solutions to the Cauchy problem for a scalar multidimensional conservation law as small diffusion limit of a stochastic perturbation along characteristics. It helps, in particular, to study the process of…

This study is devoted to proving the existence of weak solutions for a nonlinear elliptic problem with Neumann-type boundary data. The problem is driven by a discontinuous power nonlinearity and a nonsmooth prescribed data. Additionally, we…

We study the Cauchy problem for general, nonlinear, strictly hyperbolic systems of partial differential equations in one space variable. First, we re-visit the construction of the solution to the Riemann problem and introduce the notion of…

Asymptotic expansion is constructed and justified for the solution to a nonuniform Neumann boundary-value problem for the Poisson equation with the right-hand side that depends both on longitudinal and transversal variables in a thin…

The asymptotic behavior of the analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain is studied. Different asymptotic expansions with respect to the perturbation parameter and to…

In this paper, as an improvement of the paper [K. Ishige, T. Kawakami and H. Michihisa, SIAM J. Math. Anal. 49 (2017) pp. 2167--2190], we obtain the higher order asymptotic expansions of the large time behavior of the solution to the Cauchy…

We study how to identify a class of continuous-time nonlinear systems defined by an ordinary differential equation affine in the unknown parameter. We define a notion of asymptotic consistency as $(n, h) \to (\infty, 0)$, and we achieve it…

In this study linear and nonlinear higher order singularly perturbed problems are examined by a numerical approach, the differential quadrature method. Here, the main idea is using Chebyshev polynomials to acquire the weighting coefficient…

Our aim in this paper is to investigate the asymptotic behavior of solutions of the perturbed linear fractional differential system. We show that if the original linear autonomous system is asymptotically stable then under the action of…

We consider the Cauchy problem for inhomogeneous linear moment differential equations with holomorphic time dependent coefficients. Using such tools as the formal norms, theory of majorants and the properties of the Newton polygon, we…