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"We obtain local boundedness and maximum principles for weak subsolutions to certain infinitely degenerate elliptic divergence form inhomogeneous equations, and also continuity of weak solutions to homogeneous equations. For example, we consider the family {f[sigma]}[sigma]>0 with f[sigma] (x) = e -( 1 [pipe]x[pipe] ) [sigma] , -[infinity]
Differential equations, Elliptic
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Function spaces.
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Partial differential equations -- Qualitative properties of solutions -- Smoothness and regularity of solutions to PDEs.
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Partial differential equations -- Generalized solutions -- Weak solutions to PDEs.
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Partial differential equations -- Close-to-elliptic equations -- None of the above, but in this section.
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Geometry -- Metric geometry -- None of the above, but in this section.
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Functional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of "smooth'' functions, embedding theorems, trace theorems.
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Numerical solutions.
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This book is devoted to the teaching and learning of fluid mechanics. Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, mechanical, chemical and civil engineering and environmental sciences, each highlighting a different aspect or interpretation of the foundation and applications of fluids. While scholarship in fluid mechanics is vast, expanding into the areas of experimental, theoretical and computational fluid mechanics, there is little discussion among scientists about the different possible ways of teaching this subject. We think there is much to be learned, for teachers and students alike, from an interdisciplinary dialogue about fluids. This volume therefore highlights articles which have bearing on the pedagogical aspects of fluid mechanics at the undergraduate and graduate level.
Technology: general issues --- fluid dynamics education --- damped pendulums --- fluid drag --- fluid-structure interaction --- computational fluid dynamics --- outcomes competences --- hydraulic engineering --- hydraulic teaching --- active methodology --- droplet impact --- undergraduate education --- applications of fluids --- vortex formation length --- wake --- vortex shedding --- practical engineering education --- fluid mechanics --- learning and teaching --- laboratories --- data assimilation --- variational and sequential methods --- Kalman filtering --- forward sensitivity --- measurements fusion --- reduced order models --- quasi-geostrophic equations --- closure models --- Navier-Stokes equations --- Leray-Hopf weak solutions --- existence --- inquiry-based instruction --- science education --- teaching-learning sequences --- didactic transformation --- primary level --- CFD --- Julia --- Blasius --- Hiemenz --- Homann --- Falkner–Skan --- boundary-layer --- open water tank --- education --- n/a --- Falkner-Skan
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This book is devoted to the teaching and learning of fluid mechanics. Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, mechanical, chemical and civil engineering and environmental sciences, each highlighting a different aspect or interpretation of the foundation and applications of fluids. While scholarship in fluid mechanics is vast, expanding into the areas of experimental, theoretical and computational fluid mechanics, there is little discussion among scientists about the different possible ways of teaching this subject. We think there is much to be learned, for teachers and students alike, from an interdisciplinary dialogue about fluids. This volume therefore highlights articles which have bearing on the pedagogical aspects of fluid mechanics at the undergraduate and graduate level.
fluid dynamics education --- damped pendulums --- fluid drag --- fluid-structure interaction --- computational fluid dynamics --- outcomes competences --- hydraulic engineering --- hydraulic teaching --- active methodology --- droplet impact --- undergraduate education --- applications of fluids --- vortex formation length --- wake --- vortex shedding --- practical engineering education --- fluid mechanics --- learning and teaching --- laboratories --- data assimilation --- variational and sequential methods --- Kalman filtering --- forward sensitivity --- measurements fusion --- reduced order models --- quasi-geostrophic equations --- closure models --- Navier-Stokes equations --- Leray-Hopf weak solutions --- existence --- inquiry-based instruction --- science education --- teaching-learning sequences --- didactic transformation --- primary level --- CFD --- Julia --- Blasius --- Hiemenz --- Homann --- Falkner–Skan --- boundary-layer --- open water tank --- education --- n/a --- Falkner-Skan
Choose an application
This book is devoted to the teaching and learning of fluid mechanics. Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, mechanical, chemical and civil engineering and environmental sciences, each highlighting a different aspect or interpretation of the foundation and applications of fluids. While scholarship in fluid mechanics is vast, expanding into the areas of experimental, theoretical and computational fluid mechanics, there is little discussion among scientists about the different possible ways of teaching this subject. We think there is much to be learned, for teachers and students alike, from an interdisciplinary dialogue about fluids. This volume therefore highlights articles which have bearing on the pedagogical aspects of fluid mechanics at the undergraduate and graduate level.
Technology: general issues --- fluid dynamics education --- damped pendulums --- fluid drag --- fluid-structure interaction --- computational fluid dynamics --- outcomes competences --- hydraulic engineering --- hydraulic teaching --- active methodology --- droplet impact --- undergraduate education --- applications of fluids --- vortex formation length --- wake --- vortex shedding --- practical engineering education --- fluid mechanics --- learning and teaching --- laboratories --- data assimilation --- variational and sequential methods --- Kalman filtering --- forward sensitivity --- measurements fusion --- reduced order models --- quasi-geostrophic equations --- closure models --- Navier-Stokes equations --- Leray-Hopf weak solutions --- existence --- inquiry-based instruction --- science education --- teaching-learning sequences --- didactic transformation --- primary level --- CFD --- Julia --- Blasius --- Hiemenz --- Homann --- Falkner-Skan --- boundary-layer --- open water tank --- education
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This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.
heteroclinic solutions --- non-instantaneous impulses --- Schauder’s fixed point theory --- dichotomy --- second-order differential/difference/q-difference equation of hypergeometric type --- differential equations --- a priori estimates --- global solutions --- generalized Liouville equation --- Hilbert space --- dissipation --- collocation method --- exponential dichotomy --- Sumudu decomposition method --- three-step Taylor method --- dynamical system --- lower and upper solutions --- problems in the real line --- Nagumo condition on the real line --- SIRS epidemic model --- first order periodic systems --- regular solutions --- Clairin’s method --- coupled nonlinear systems --- Navier–Stokes equations --- Bäcklund transformation --- asymptotic stability --- Caputo fractional derivative --- exponential stability --- difference equations --- lipschitz stability --- strong nonlinearities --- polynomial solution --- integro-differentials --- kinetic energy --- Legendre wavelets --- weak solutions --- discrete Lyapunov equation --- population dynamics --- non-uniform lattices --- Korteweg-de Vries equation --- time-dependent partial differential equations --- mean curvature operator --- functional boundary conditions --- mathematical modelling --- fixed point theory --- limit-periodic solutions --- Arzèla Ascoli theorem --- Miura transformation --- state dependent delays --- ?-Laplacian operator --- divided-difference equations --- effective existence criteria
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