Related papers: On the wellposedness of the exp-Rabelo equation
The short pulse equation provides a model for the propagation of the ultra-short light pulse in silica optical fibers It is a nonlinear evolution equation. In this paper the wellposedness of bounded solutions for the inhomogeneous initial…
The short pulse equation provides a model for the propagation of ultra-short light pulses in silica optical fibers. It is a nonlinear evolution equation. In this paper the wellposedness of bounded solutions for the homogeneous initial…
We prove local well-posedness in the Sobolev spaces $\dot H^s(\mathbb{T})$, with $s>7/2$, for an initial value problem for a nonlocal, cubically nonlinear, dispersive equation that provides an approximate description of the evolution of…
We study four distinct second-order nonlinear equations of Rabelo which describe pseudospherical surfaces. By transforming these equations to the constant-characteristic form we relate them to some well-studied integrable equations. Two of…
In this article, we show that a technique for showing well-posedness results for evolutionary equations in the sense of [13] established in [16] applies to a broader class of non-autonomous integro-differential-algebraic equations. Using…
Variable-exponent fractional models attract increasing attentions in various applications, while the rigorous analysis is far from well developed. This work provides general tools to address these models. Specifically, we first develop a…
It is well known that, under standard assumptions, initial value problems for fractional ordinary differential equations involving Caputo-type derivatives are well posed in the sense that a unique solution exists and that this solution…
The initial value problem for some defocusing coupled nonlinear Schrodinger equations is investigated. Global well-posedness and scattering are established.
This article is a comparative study on an initial-boundary value problem for a class of semilinear pseudo-parabolic equations with the fractional Caputo derivative, also called the fractional Sobolev-Galpern type equations. The purpose of…
This paper presents a mathematical foundation for physical models in nonlinear optics through the lens of evolutionary equations. It focuses on two key concepts: well-posedness and exponential stability of Maxwell equations, with models…
In this paper we study boundary value problems for higher order elliptic differential operators in divergence form. We establish well posedness for problems with boundary data in Besov spaces $\dot B^{p,p}_s$, $p\leq 1$, given well…
We review the concept of well-posedness in the context of evolutionary problems from mathematical physics for a particular subclass of problems from elasticity theory. The complexity of physical phenomena appears as encoded in so called…
Well-posedness is studied for a special system of two-point boundary value problem for evolution equations which is called a forward-backward evolution equation (FBEE, for short). Two approaches are introduced: A decoupling method with some…
In this thesis we consider so-called linear evolutionary problems, a class of linear partial differential equations covering classical elliptic, parabolic and hyperbolic equations from mathematical physics as well as classes of…
In this paper, we study the well-posedness of boundary value problems for a special class of degenerate elliptic equations coming from geometry. Such problems is intimately tied to rigidity problem arising in infinitesimal isometric…
We study a model elliptic pseudo-differential equation and simplest boundary value problems for a half-space and a special cone in Sobolev--Slobodetskii spaces which have different smoothness with respect to separate variables. Sufficient…
We derive a system of equations which can be seen as an evolving surface version of the diffuse interface "Model H" of Hohenberg and Halperin (1977). We then consider the well-posedness for the corresponding (tangential) system when one…
These lecture notes accompany two classes given at the NRHEP2 school. In the first lecture I introduce the basic concepts used for analyzing well-posedness, that is the existence of a unique solution depending continuously on given data, of…
We consider the initial value problem associated to the regularized Benjamin-Ono equation, rBO. Our aim is to establish local and global well-posedness results in weighted Sobolev spaces via contraction principle. We also prove a unique…
In this paper, we consider a system of partial differential equations modeling the evolution of a landscape. A ground surface is eroded by the flow of water over it, either by sedimentation or dilution. The system is composed by three…