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We study a family of nonlinear initial value partial differential equations in the complex domain under the action of two asymmetric time variables. Different Gevrey bounds and multisummability results are obtain depending on each element…

Complex Variables · Mathematics 2018-06-21 Alberto Lastra , Stéphane Malek

We consider a coupled system of two singularly perturbed reaction-diffusion equations, with two small parameters $0< \epsilon \le \mu \le 1$, each multiplying the highest derivative in the equations. The presence of these parameters causes…

Numerical Analysis · Mathematics 2015-03-19 Jens Markus Melenk , Christos Xenophontos , Lisa Oberbroeckling

In this article we study the asymptotic behavior, of the solution of a nonlinear elliptic, anisotropic singular perturbations problem in cylindrical domain, the limit problem is given and strong convergences are proved, we also give an…

Analysis of PDEs · Mathematics 2014-10-08 Ogabi Chokri

In this paper we classify the pathwise asymptotic behaviour of the discretisation of a general autonomous scalar differential equation which has a unique and globally stable equilibrium. The underlying continuous equation is subjected to a…

Probability · Mathematics 2013-10-10 John A. D. Appleby , Jian Cheng , Alexandra Rodkina

This article proves the existence and regularity of weak solutions for a class of mixed local-nonlocal problems with singular nonlinearities. We examine both the purely singular problem and perturbed singular problems. A central…

Analysis of PDEs · Mathematics 2025-02-27 Sanjit Biswas , Prashanta Garain

In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…

Classical Analysis and ODEs · Mathematics 2020-02-17 H. T. Tuan , S. Siegmund

We study the symmetry properties of the weak positive solutions to a class of quasi-linear elliptic problems having a variational structure. On this basis, the asymptotic behaviour of global solutions of the corresponding parabolic…

Analysis of PDEs · Mathematics 2009-10-09 Luigi Montoro , Berardino Sciunzi , Marco Squassina

Properties of solutions of generic hyperbolic systems with multiple characteristics with diagonalizable principal part are investigated. Solutions are represented as a Picard series with terms in the form of iterated Fourier integral…

Analysis of PDEs · Mathematics 2008-02-05 Ilia Kamotski , Michael Ruzhansky

Fractional derivatives of Prabhakar type are capturing an increasing interest since their ability to describe anomalous relaxation phenomena (in dielectrics and other fields) showing a simultaneous nonlocal and nonlinear behaviour. In this…

Numerical Analysis · Mathematics 2020-08-13 Roberto Garrappa , Eva Kaslik

In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential…

Classical Analysis and ODEs · Mathematics 2018-08-24 Kai Diethelm , Stefan Siegmund , H. T. Tuan

An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…

Dynamical Systems · Mathematics 2023-05-29 Oskar A. Sultanov

A solution to the ultra-relativistic strong explosion problem with a non-power law density gradient is delineated. We consider a blast wave expanding into a density profile falling off as a steep radial power-law with small, spherically…

High Energy Astrophysical Phenomena · Physics 2014-11-20 Yonatan Oren , Re'em Sari

This paper studies the dynamics of families of monotone nonautonomous neutral functional differential equations with nonautonomous operator, of great importance for their applications to the study of the long-term behavior of the…

Dynamical Systems · Mathematics 2020-04-06 Sylvia Novo , Rafael Obaya , Victor M. Villarragut

We study some properties concerning the asymptotic behavior of solutions to nonautonomous retarded functional differential equations, depending on the knowledge of certain solutions of the associated generalized characteristic equation.

Classical Analysis and ODEs · Mathematics 2010-08-05 Claudio Cuevas , Miguel V. S. Frasson

In this note we are dealing with the problem of existence and asymptotic behavior of solutions for the non-resonant singularly perturbed linear Neumann boundary value problem \begin{eqnarray*} \epsilon y"+ky=f(t),\quad k>0,\quad…

Classical Analysis and ODEs · Mathematics 2017-09-08 Robert Vrabel

We analyze the spatial structure of asymptotics of a solution to a singularly perturbed system of mass transfer equations. The leading term of the asymptotics is described by a parabolic equation with possibly degenerate spatial part. We…

Analysis of PDEs · Mathematics 2021-10-12 Vitaly A. Krasikov , Andrey V. Nesterov

We study a linear $q-$difference-differential Cauchy problem, under the action of a perturbation parameter $\epsilon$. This work deals with a $q-$analog of the research made in a previoues work, giving rise to a generalization of a recent…

Complex Variables · Mathematics 2015-08-12 Alberto Lastra , Stéphane Malek

Results of investigation of the asymptotic behavior of solutions to the Cauchy problems for a quasi-linear parabolic equation with a small parameter at a higher derivative near singular points of limit solutions are presented. Interest to…

Mathematical Physics · Physics 2014-11-18 Sergei V. Zakharov

In this paper we study the conditions for the existence of strong solutions (both local and global) for stochastic bidomain equations. To this end, we use apriori energy estimates and Serrin-type theorems. We further address the asymptotic…

Analysis of PDEs · Mathematics 2021-11-15 Oleksiy Kapustyan , Oleksandr Misiats , Oleksandr Stanzhytskyi

In this paper, we review several results from singularly perturbed differential equations with multiple small parameters. In addition, we develop a general conceptual framework to compare and contrast the different results by proposing a…