Singular Solutions of Protter’s Problem for a Class of 3-D Hyperbolic Equations

Недю Иванов Попиванов, Алексей Йорданов Николов - През 1952 г. М. Протър формулира нови гранични задачи за вълновото уравнение, които са тримерни аналози на задачите на Дарбу в равнината. Задачите са разгледани в тримерна област, ограничена от две характеристични конуса и равнина. Сега, след като са минали повече от 50 години, е добре известно, че за безброй гладки функции в дясната страна на уравнението тези задачи нямат класически решения, а обобщеното решение има силна степенна особеност във върха на характеристичния конус, която е изолирана и не се разпространява по конуса. Тук ние разглеждаме трета гранична задача за вълновото уравнение с младши членове и дясна страна във формата на тригонометричен полином. Дадена е по-нова от досега известната априорна оценка за максимално възможната особеност на решенията на тази задача. Оказва се, че при по-общото уравнение с младши членове възможната сингулярност е от същия ред като при чисто вълновото уравнение.

Hyperbolic Double-Complex Laplace Operator

2010 Mathematics Subject Classification: 35G35, 32A30, 30G35.

Hyperbolic Fibrations and PDE

2010 Mathematics Subject Classification: 35L10, 35L90.

Weak Convergence to the Tangent Process of the Linear Multifractional Stable Motion

2000 Mathematics Subject Classification: 60G18, 60E07

Anomalous Singularities for Hyperbolic Equations with Degeneracy of Infinite Order

2002 Mathematics Subject Classification: 35L80

About Strictly Hyperbolic Operators with Non-Regular Coefficients

2002 Mathematics Subject Classification: 35L15, 35L80, 35S05, 35S30

On the Zeros of the Solutions to Nonlinear Hyperbolic Equations with Delays

2002 Mathematics Subject Classification: Primary 35В05; Secondary 35L15

On The Cauchy Problem for Non Effectively Hyperbolic Operators, The Ivrii-Petkov-Hörmander Condition and the Gevrey Well Posedness

2000 Mathematics Subject Classification: 35L15, Secondary 35L30.

On an ODE Relevant for the General Theory of the Hyperbolic Cauchy Problem

2000 Mathematics Subject Classification: 34E20, 35L80, 35L15.

Even and Old Overdetermined Strata for Degree 6 Hyperbolic Polynomials

2000 Mathematics Subject Classification: 12D10.

Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials

MSC 2010: 30C10, 32A30, 30G35

A kvázi- és általánosított hiperbolikus diszkontálás hosszú távon (Quasi- and Generalized Hyperbolic Discounting in Long Term)

Az intertemporális döntések fontos szerepet játszanak a közgazdasági modellezésben, és azt írják le, hogy milyen átváltást alkalmazunk két különböző időpont között. A közgazdasági modellezésben az exponenciális diszkontálás a legelterjedtebb, annak ellenére, hogy az empirikus vizsgálatok alapján gyenge a magyarázó ereje. A gazdaságpszichológiában elterjedt általánosított hiperbolikus diszkontálás viszont nagyon nehezen alkalmazható közgazdasági modellezési célra. Így tudott gyorsan elterjedni a kvázi-hiperbolikus diszkontálási modell, amelyik úgy ragadja meg a főbb pszichológiai jelenségeket, hogy kezelhető marad a modellezés során. A cikkben azt állítjuk, hogy hibás az a megközelítés, hogy hosszú távú döntések esetén, főleg sorozatok esetén helyettesíthető a két hiperbolikus diszkontálás egymással. Így a hosszú távú kérdéseknél érdemes felülvizsgálni a kvázi-hiperbolikus diszkontálással kapott eredményeket, ha azok az általánosított hiperbolikus diszkontálási modellel való helyettesíthetőséget feltételezték. ____ Intertemporal choice is one of the crucial questions in economic modeling and it describes decisions which require trade-offs among outcomes occurring in different points in time. In economic modeling the exponential discounting is the most well known, however it has weak validity in empirical studies. Although according to psychologists generalized hyperbolic discounting has the strongest descriptive validity it is very complex and hard to use in economic models. In response to this challenge quasi-hyperbolic discounting was proposed. It has the most important properties of generalized hyperbolic discounting while tractability remains in analytical modeling. Therefore it is common to substitute generalized hyperbolic discounting with quasi-hyperbolic discounting. This paper argues that the substitution of these two models leads to different conclusions in long term decisions especially in the case of series; hence all the models that use quasi-hyperbolic discounting for long term decisions should be revised if they states that generalized hyperbolic discounting model would have the same conclusion.

Cornered Asymptotically Hyperbolic Metrics

Thesis (Ph.D.)--University of Washington, 2016-08