Singular perturbations and boundary layers

분야Field	Math Colloquium
날짜Date	2019-05-03 ~ 2019-05-03	시간Time	15:50 ~ 18:00
장소Place	Math. Bldg. 404	초청자Host	권재룡
연사Speaker	Chang Yeol Jung	소속Affiliation	UNIST
TOPIC	Singular perturbations and boundary layers
소개 및 안내사항Content	1부 Title: Singular perturbations and boundary layers Abstract: Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations. From the physical point of view, singular perturbations generate in the system under consideration thin layers located often but not always at the boundary of the domains that are called boundary layers or internal layers if the layer is located inside the domain. Important physical phenomena occur in boundary layers. The most common boundary layers appear in fluid mechanics, e.g., the flow of air around an airfoil or a whole airplane or the flow of air around a car. In these cases, the boundary layer is a very small thin layer of air, barely visible, in which the velocity of air varies very rapidly from the cruise velocity to the zero velocity. Singular perturbations occur in many other phenomena, like rotating flows, geophysical flows, e.g., the air-ocean interface, in acoustics, electromagnetism, or lasers. 2부 Title: Approximating the solutions to Euler-Poisson systems with boundary layers Abstract: We aim to construct the approximate solutions to a Euler-Poisson system in an annular domain. A small parameter, multiplied to the highest order derivatives in the system, produces a singular behavior of the solutions. Among others, the sharp transitions near boundaries which are called boundary layers can occur. We explicitly construct the approximate solutions composed of the outer and inner expansions in the order of the small parameter. The equations for describing the boundary layers are determined from the inner expansions. In addition, here we effectively treat nonlinear terms using the Taylor polynomial expansions with multinomials. We also provide numerical evidence demonstrating the convergence of the approximate solutions to those of the Euler-Poisson system as the small parameter goes to zero.

학회명Field	Singular perturbations and boundary layers
날짜Date	2019-05-03 ~ 2019-05-03	시간Time	15:50 ~ 18:00
장소Place	Math. Bldg. 404	초청자Host	권재룡
소개 및 안내사항Content	1부 Title: Singular perturbations and boundary layers Abstract: Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations. From the physical point of view, singular perturbations generate in the system under consideration thin layers located often but not always at the boundary of the domains that are called boundary layers or internal layers if the layer is located inside the domain. Important physical phenomena occur in boundary layers. The most common boundary layers appear in fluid mechanics, e.g., the flow of air around an airfoil or a whole airplane or the flow of air around a car. In these cases, the boundary layer is a very small thin layer of air, barely visible, in which the velocity of air varies very rapidly from the cruise velocity to the zero velocity. Singular perturbations occur in many other phenomena, like rotating flows, geophysical flows, e.g., the air-ocean interface, in acoustics, electromagnetism, or lasers. 2부 Title: Approximating the solutions to Euler-Poisson systems with boundary layers Abstract: We aim to construct the approximate solutions to a Euler-Poisson system in an annular domain. A small parameter, multiplied to the highest order derivatives in the system, produces a singular behavior of the solutions. Among others, the sharp transitions near boundaries which are called boundary layers can occur. We explicitly construct the approximate solutions composed of the outer and inner expansions in the order of the small parameter. The equations for describing the boundary layers are determined from the inner expansions. In addition, here we effectively treat nonlinear terms using the Taylor polynomial expansions with multinomials. We also provide numerical evidence demonstrating the convergence of the approximate solutions to those of the Euler-Poisson system as the small parameter goes to zero.

성명Field	Singular perturbations and boundary layers
날짜Date	2019-05-03 ~ 2019-05-03	시간Time	15:50 ~ 18:00
소속Affiliation	UNIST	초청자Host	권재룡
소개 및 안내사항Content	1부 Title: Singular perturbations and boundary layers Abstract: Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations. From the physical point of view, singular perturbations generate in the system under consideration thin layers located often but not always at the boundary of the domains that are called boundary layers or internal layers if the layer is located inside the domain. Important physical phenomena occur in boundary layers. The most common boundary layers appear in fluid mechanics, e.g., the flow of air around an airfoil or a whole airplane or the flow of air around a car. In these cases, the boundary layer is a very small thin layer of air, barely visible, in which the velocity of air varies very rapidly from the cruise velocity to the zero velocity. Singular perturbations occur in many other phenomena, like rotating flows, geophysical flows, e.g., the air-ocean interface, in acoustics, electromagnetism, or lasers. 2부 Title: Approximating the solutions to Euler-Poisson systems with boundary layers Abstract: We aim to construct the approximate solutions to a Euler-Poisson system in an annular domain. A small parameter, multiplied to the highest order derivatives in the system, produces a singular behavior of the solutions. Among others, the sharp transitions near boundaries which are called boundary layers can occur. We explicitly construct the approximate solutions composed of the outer and inner expansions in the order of the small parameter. The equations for describing the boundary layers are determined from the inner expansions. In addition, here we effectively treat nonlinear terms using the Taylor polynomial expansions with multinomials. We also provide numerical evidence demonstrating the convergence of the approximate solutions to those of the Euler-Poisson system as the small parameter goes to zero.

성명Field	Singular perturbations and boundary layers
날짜Date	2019-05-03 ~ 2019-05-03	시간Time	15:50 ~ 18:00
호실Host		인원수Affiliation	Chang Yeol Jung
사용목적Affiliation	권재룡	신청방식Host	UNIST
소개 및 안내사항Content	1부 Title: Singular perturbations and boundary layers Abstract: Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations. From the physical point of view, singular perturbations generate in the system under consideration thin layers located often but not always at the boundary of the domains that are called boundary layers or internal layers if the layer is located inside the domain. Important physical phenomena occur in boundary layers. The most common boundary layers appear in fluid mechanics, e.g., the flow of air around an airfoil or a whole airplane or the flow of air around a car. In these cases, the boundary layer is a very small thin layer of air, barely visible, in which the velocity of air varies very rapidly from the cruise velocity to the zero velocity. Singular perturbations occur in many other phenomena, like rotating flows, geophysical flows, e.g., the air-ocean interface, in acoustics, electromagnetism, or lasers. 2부 Title: Approximating the solutions to Euler-Poisson systems with boundary layers Abstract: We aim to construct the approximate solutions to a Euler-Poisson system in an annular domain. A small parameter, multiplied to the highest order derivatives in the system, produces a singular behavior of the solutions. Among others, the sharp transitions near boundaries which are called boundary layers can occur. We explicitly construct the approximate solutions composed of the outer and inner expansions in the order of the small parameter. The equations for describing the boundary layers are determined from the inner expansions. In addition, here we effectively treat nonlinear terms using the Taylor polynomial expansions with multinomials. We also provide numerical evidence demonstrating the convergence of the approximate solutions to those of the Euler-Poisson system as the small parameter goes to zero.