Wave operators and asymptotic solutions of the d'Alembert equation in exterior domains

Equations for a potentiostatic reaction with an adsorption process following Langmuir’s isotherm have been derived for the expanding sphere with any power law electrode model. This model is very general and includes, among others, the following ones: (a) stationary plane; (b) stationary sphere; (c) expanding plane; and (d) expanding sphere. Characteristics of these solutions and the behavior of the corresponding asymptotic solutions are discussed. A comparison of the results obtained for plane and spherical electrodes has also been performed.

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Global existence of null-form wave equations in exterior domains

Mathematische Zeitschrift ◽

10.1007/s00209-006-0083-2 ◽

2007 ◽

Vol 256 (3) ◽

pp. 521-549 ◽

Cited By ~ 35

Author(s):

Jason Metcalfe ◽

Christopher D. Sogge

Keyword(s):

Global Existence ◽

Wave Equations ◽

Exterior Domains

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Global existence of solutions to a weakly coupled critical parabolic system in two-dimensional exterior domains

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2021.125214 ◽

2021 ◽

pp. 125214

Author(s):

Motohiro Sobajima

Keyword(s):

Global Existence ◽

Parabolic System ◽

Existence Of Solutions ◽

Two Dimensional ◽

Exterior Domains ◽

Global Existence Of Solutions ◽

Weakly Coupled

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Large Time Decay of Solutions to a Linear Nonautonomous System in Exterior Domains

Mathematics ◽

10.3390/math9080841 ◽

2021 ◽

Vol 9 (8) ◽

pp. 841

Author(s):

Toshiaki Hishida

Keyword(s):

Evolution Operator ◽

Large Time ◽

Rigid Motion ◽

Time Dependent ◽

Energy Relation ◽

Exterior Domains ◽

Decay Properties ◽

Decay Of Solutions ◽

Whole Space ◽

Expository Paper

In this expository paper, we study Lq-Lr decay estimates of the evolution operator generated by a perturbed Stokes system in n-dimensional exterior domains when the coefficients are time-dependent and can be unbounded at spatial infinity. By following the approach developed by the present author for the physically relevant case where the rigid motion of the obstacle is time-dependent, we clarify that some decay properties of solutions to the same system in whole space Rn together with the energy relation imply the desired estimates in exterior domains provided n≥3.

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