Las ecuaciones de Boussinesq son un tipo de ecuaciones derivadas de las ecuaciones de Euler y que modelan la propagación sensiblemente bidimensional de ondas largas de gravedad y de pequeña amplitud sobre la super cie de un canal. Un modelo de este tipo en un canal de fondo plano está dado por el sistema (P1)donde las variables adimensionales y w representan respectivamente, la de flección de la super ficie libre del líquido respecto a su posición de reposo y la velocidad horizontal del fluido a una profundidad de raíz cuadrada 2/3h; donde h es la profundidad del fluido en reposo. Dicho modelo es desde luego un sistema de ecuaciones diferenciales de Korteweg-de Vries acopladas a través de los efectos dispersivos y los términos no lineales. Por otro lado, el sistema (P1) al estar referido a un fl uido incompresible no viscoso no recoge los efectos de la viscosidad ; sin embargo al ser desacoplado podemos introducir tales efectos, resultando un sistema del tipo Korteweg-de Vries - Burger dado por (P2) En este trabajo se estudia el PVI asociado a (P2) en los espacios Hs estableciendo su buena formulación local para s > 3/2 y buena formulación global para s >= 2; en este último caso se muestra adicionalmente que la solución global decae asíntoticamente en el tiempo. Finalmente, se muestra que el PVI asociado a (P1) está bien formulado localmente como consecuencia de la buena formulación local de (P2). / Tesis

No description available.

En este traba jo se ha e un estudio a era de la Teoría de perturbación de operadores disipativos para probar la existencia de soluciones de un sistema a acoplado de KdV Lineal en un intervalo a acotado con disipación localizada. Para tal finalidad hacemos uso de la Teoría de Semigrupos, estimativas de energía, técnicas multiplicativas y Propiedad de Continuación Única, demostrando el decaimiento exponencial de la solución. -- PALABRAS CLAVES: TEOREMA DE LUMMER PHILLIPS, TEORÍA DE PERTURBACIÓN, DECAIMIENTO EXPONENCIAL, PROPIEDAD DE CONTINUACIÓN ÚNICA. / --- In this work we use Semigroup Theory and Perturbation Theory of dissipative operators in order to prove the existen e and uniquess of a solution of a oupled linear system of the Korteweg-de Vries equations in a bounded interval with lo alized damping, we use multiplier te hniques, energy estimates. Finally, we apply the Unique Continuation Property to prove the exponential de ay of solutions.

El objetivo principal en este trabajo es estudiar el comportamiento asint´otico en el tiempo de las soluciones del problema de valor inicial ∂ᵘt+ ∂ᶟᵪu + α∂ᶟᵪv + uᵖ∂ᵪu + vp∂ᵛᵪ = 0 ∂tᵛ + ∂ᶟᵪ v + α∂ᶟᵪu + vᵖ∂ᵪᵛ + ∂ᵪ (uvᵖ) = 0 u (x, 0) = u₀ v (x, 0) = v₀, donde α es una constante real menor que 1. El sistema se considera para x ∈ R y t ≥ 0. El exponente p es un entero mayor o igual a 1. El sistema tiene la estructura de un par de ecuaciones de Korteweg-de Vries generalizadas acopladas a través de ambos efectos dispersivos y no lineales, y es un caso particular del sistema derivado por Gear y Grimshaw como un modelo para describir la interacción fuerte de ondas largas débilmente no lineales. Para esto se demuestra, mediante la teoría de T. Kato para ecuaciones de evolución cuasi lineales del tipo hiperbólico, que el problema está bien formulado localmente en los espacios clásicos de Sobolev Hs (R) × Hs (R) para s ≥ 3. Usando el método de la fase estacionaria analizamos la parte lineal del sistema y entonces usando la versión integral de nuestro problema se genera el siguiente resultado: existe una constante C > 0 tal que: II(u, v) (t)IIH³͚ ≤ C (1 + t)-⅓ cuando t → ∞, suponiendo que el dato inicial en t = 0 satisface las condiciones para p ≥ 4 y |α| < 1. / Tesis

El objetivo principal en este trabajo es estudiar el comportamiento asint´otico en el tiempo de las soluciones del problema de valor inicial ∂ᵘt+ ∂ᶟᵪu + α∂ᶟᵪv + uᵖ∂ᵪu + vp∂ᵛᵪ = 0 ∂tᵛ + ∂ᶟᵪ v + α∂ᶟᵪu + vᵖ∂ᵪᵛ + ∂ᵪ (uvᵖ) = 0 u (x, 0) = u₀ v (x, 0) = v₀, donde α es una constante real menor que 1. El sistema se considera para x ∈ R y t ≥ 0. El exponente p es un entero mayor o igual a 1. El sistema tiene la estructura de un par de ecuaciones de Korteweg-de Vries generalizadas acopladas a través de ambos efectos dispersivos y no lineales, y es un caso particular del sistema derivado por Gear y Grimshaw como un modelo para describir la interacción fuerte de ondas largas débilmente no lineales. Para esto se demuestra, mediante la teoría de T. Kato para ecuaciones de evolución cuasi lineales del tipo hiperbólico, que el problema está bien formulado localmente en los espacios clásicos de Sobolev Hs (R) × Hs (R) para s ≥ 3. Usando el método de la fase estacionaria analizamos la parte lineal del sistema y entonces usando la versión integral de nuestro problema se genera el siguiente resultado: existe una constante C > 0 tal que: II(u, v) (t)IIH³͚ ≤ C (1 + t)-⅓ cuando t → ∞, suponiendo que el dato inicial en t = 0 satisface las condiciones para p ≥ 4 y |α| < 1. / Tesis

In this thesis we prove polynomial-in-time upper bounds for the orbital instability of solitons for subcritical generalized Korteweg-de Vries equations in $H^{s}_{x}(\mathbb{R})$ with $s < 1$. By combining coercivity estimates of Weinstein with the $I$-method as developed by Colliander, Keel, Staffilani, Takaoka, and Tao, we construct a modified energy functional which is shown to be almost conserved while providing us with an estimate of the deviation of the solution from the ground state curve. The iteration of the almost conservation law for the modified energy functional over time intervals of uniform length yields the polynomial upper bound.

In this thesis we prove polynomial-in-time upper bounds for the orbital instability of solitons for subcritical generalized Korteweg-de Vries equations in $H^{s}_{x}(\mathbb{R})$ with $s < 1$. By combining coercivity estimates of Weinstein with the $I$-method as developed by Colliander, Keel, Staffilani, Takaoka, and Tao, we construct a modified energy functional which is shown to be almost conserved while providing us with an estimate of the deviation of the solution from the ground state curve. The iteration of the almost conservation law for the modified energy functional over time intervals of uniform length yields the polynomial upper bound.

Thesis (Ph. D.)--Oregon State University, 2004. / Typescript (photocopy). Includes bibliographical references (leaves 73-75). Also available on the World Wide Web.

Onder letterkundiges word De Vries vandag allerweë as een van die belangrikste Afrikaanse kortkunsbeoefenaars beskou. Uitgaande van 'n ondersoek na die vertellersperspektief as orienterende element, wil hierdie studie De Vries se ontwikkeling van bundel tot bundel volg en vasstel of hy die aandag verdien wat hom vandag te beurt val. In Hoog teen die heuningkrans (1956) is De Vries se talent op sy ongevormdste. Hiervan is die naïwe benutting van die vertellersperspektief, soos veral blyk in "Alles vir die klein dingetjies" en "Die rooi vaas", duidelike bewys. Verlore erwe (1959) vertoon nie 'n beduidende vooruitgang op sy debuutbundel nie. Wat hierin wel opval, is die eerste tekens om d.m.v. suggestie die lesersbetrokkenheid (in "'n Kloof soos Varingkloof" en "Pêrels voor die swyne") te verhoog. Hierop bou De Vries voort in Vetkers en neonlig (1960). Hierdie bundel vertoon ook 'n duideliker merkbare ontginning van die verteller as struktuurelement, soos uit 'n ontleding van "Die gusooi", "Vader en seun" en "Skoenemaker , diepe water" duidelik word. Daarbenewens tree daar met hierdie bundel tematiese vernuwing in De Vries se werk in: die lokale realisme van vroeër maak plek vir 'n meer fantastiese ( "Skoenemaker") en gewelddadig/ makabere ("Die turksvyrant", "Die gusooi" en "Vader en seun") bewerking van sy stof. Met Dubbeldoor (1963) sit De Vries hierdie stygende ontwikkelingslyn voort. Hy beheer die vertellersperspektief met groter gemak en sy verhale vertoon 'n fyner afgerondheid. Die bundel se hoogtepunte is geleë in die verhale in die eerstepersoon bv. "Brood: variasie op 'n tema" en "Stamme vir die ruimte". Vliegoog (1965) is De Vries se hoogtepunt uit die jare sestig. In verhaal na verhaal, deur die hantering veral van verskillende vertellersperspektiewe, blyk sy bekwame vakmanskap. Verhale wat hier uitgesonder word, is "Vlieë soek nie", "Jy moet jou by kry voor die kanon skiet", "Stasie" en "Huisbesoek van 'n grapjas". Na 'n ondersoek van die vier "Kort verhale in die eerste persoon" - uit Twee maal om die son (1969) - word tot die gevolgtrekking gekom dat De Vries onder eerste persoon ook die abstrakte outeur insluit. 'n Analise van "Terug na die natuur" bring aan die lig dat die konkrete outeur, d.m.v. subtiele manipulering van die abstrakte outeur, as karakter in die verhaal ingebring word. In hoofstuk vyf word gekyk na die eenheidskeppende elemente in De Vries se kontreikuns, waar onder Dorp in die Klein Karoo (1966), Briekwa (1973) en afdeling twee van Bliksoldate bloei nie (1975) ingesluit word. Hierin speel veral die kontrei en die persoon van die konkrete outeur 'n belangrike rol. Daar word ook uitgewys dat Briekwa, naas die kortverhale wat deur 'n brief aan mekaar verbind word, demonstrasie is van 'n skrywer se "oorlewing van die winter in hom". Met De Vries se jongste bundel, Die uur van die idiote (1980), bevestig hy sy meesterskap. Daar word bevind dat die verhaal "Raam" 'n hoogtepunt vorm t.o.v. die hantering van die vertellersperspektief. Die persoon van die konkrete outeur word op verbluffende wyse in die verhaal geïntegreer. Ten slotte word besluit dat De Vries se talent die aandag wat hom te beurt val, regverdig. ENGLISH : Amongst men of letters Abraham H. de Vries is today widely regarded as one of the most important Afrikaans short story writers. With research into the point of view as orientating element, as vantage point, this study purposes to follow De Vries's development from collection to collection to ascertain whether he deserves the attention accorded him today. In Hoog teen die heuningkrans (1956) De Vries's talent is at its most untrained. Proof is the naïve utilisation of point of view in e.g. "Alles vir die klein dingetjies" and "Die rooi vaas". Verlore erwe (1958) does not show significant improvement on his début. What is striking here, however, is the first indications of heightening readers' participation through suggestion in "'n Kloof soos Varingkloof" and "Pêrels voor die swyne". On this De Vries builds in Vetkers en neonlig (1960). This collection shows a more marked exploitation of the narrator as structural element, as is clearly indicated in an analysis of "Die gusooi", "Vader en seun" and "Skoenemaker, diepe water". In addition to this, De Vries's work also shows thematic novelties in this collection: the local realism of earlier work makes way for the more fantastic ("Skoenemaker") and violent/macabre ("Die Turksvyrant", "Die gusooi" and "Vader en seun"). With Dubbeldoor (1963) De Vries continues this ascending course of development. He commands the point of view with greater ease and his stories show a finer finish. The highlights of this collection are the stories told in the first person e.g. "Brood: variasie op 'n tema" and "Stamme vir die ruimte". Vliegoog (1965) is De Vries's peak performance in the Sixties. In story after story his mastership is indicated by especially his handling of the various points of view. Stories warranting exception here, are "Vlieë soek nie", "Jy moet jou by kry voor die kanon skiet", "Stasie" and "Huisbesoek van 'n grapjas". After research into the four "Kort verhale in die eerste persoon" from Twee maal om die son (1969) the conclusion is reached that De Vries also includes the implied author under first person. An analysis of "Terug na die natuur" shows that the concrete author, by subtle manipulation of the implied author, is brought as character into the story. In chapter five the unity of the creative elements in De Vries's "kortkuns" (regional stories), including Dorp in die Klein Karoo (1966), Briekwa (1973) and section two of Bliksoldate bloei nie (1980), are looked at. In these stories the "kontrei" (region) and the person of the concrete author play important parts. It is also shown that Briekwa, in addition to the short stories linked together by a letter, demonstrates a writer's "survival" of the "winter in himself". With De Vries's newest collection, Die uur van die idiote (1980), hy consolidates his mastership. It is found that the story "Raam" constitutes a definite pinnacle as far as handling of the point of view is concerned. The person of the concrete author is astonishingly integrated into the narrative. In conclusion it is decided that De Vries's talent warrants the attention accorded him. / Dissertation (MA)--University of Pretoria, 1983. / Afrikaans / unrestricted

Ferroelectric liquid crystals (FLCs) have been investigated as the basis for a new type of liquid crystal display because of their fast switching times. In applications the layer contraction at the smectic A-smectic C transition is a severe problem that leads to buckling of the smectic layers and results in zigzag defects that drastically degrade the optical quality of FLC films. To solve this problem, researchers are focusing on a new class of liquid crystals with minimal smectic layer contraction at the SmA-SmC transition which is referred to as ‘de Vries-like’. In the first part of this thesis, we have developed a rational design strategy based on a concept of frustration between two structural elements, one promoting a SmA phase and another promoting a SmC phase. In this chapter, we show that one can further improve ‘de Vries-like’ properties by substituting the 2-phenylpyrimidine core in our first-generation siloxane-terminated mesogens with one stronger SmC-promoting core. We also address the hydrolytic instability of siloxane-terminated mesogens, by substituting the siloxane with a carbosilane end-group. As a result of this study, we found QL6-6 that forms a SmC phase at room temperature with ‘de Vries-like’ properties that are comparable to those of bona fide ‘de Vries-like’ liquid crystals. Next, the dialkoxy 2-phenyl-1,3,4-thiadiazole core which is a very powerful SmC promoting element was investigated. We prepared the analogue of QL6-6, compound QL13-6, which only forms a SmC phase despite having a chloro-terminated alkyl chain. Making a ‘de Vries-like’ liquid crystal without carbosilane terminal side-chain was also attempted, although ultimately unsuccessful. The terminal group effect on the ‘de Vries-like’ properties was also investigated. We prepared a series of mesogens derived from 2-phenylpyridine core with different end-groups to investigate whether the X-group might interact with the core in a bilayer structure. Finally, we inves¬tigated the effect of mixing ’de Vries-like’ liquid crystals with conventional smectic liquid crystals. We show that binary mix¬tures of ‘de Vries-like’ and conventional SmC meso¬gens with a molecular length ratio of 1.34 undergo a SmA-SmC phase transition with a maximum layer contraction ranging from 1.0 to 1.9% depending on the mixture composition. / Thesis (Ph.D, Chemistry) -- Queen's University, 2013-10-29 13:16:29.768