PHRAGM&#201;N-LINDEL&#214;F ALTERNATIVE FOR THE LAPLACE EQUATION WITH DYNAMIC BOUNDARY CONDITIONS

Mari Carme Leseduarte; Ramon Quintanilla

doi:10.11948/2017081

2017 Volume 7 Issue 4

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Mari Carme Leseduarte, Ramon Quintanilla. PHRAGMÉN-LINDELÖF ALTERNATIVE FOR THE LAPLACE EQUATION WITH DYNAMIC BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1323-1335. doi: 10.11948/2017081

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Mari Carme Leseduarte, Ramon Quintanilla. PHRAGMÉN-LINDELÖF ALTERNATIVE FOR THE LAPLACE EQUATION WITH DYNAMIC BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2017, 7(4): 1323-1335. doi: 10.11948/2017081

PHRAGMÉN-LINDELÖF ALTERNATIVE FOR THE LAPLACE EQUATION WITH DYNAMIC BOUNDARY CONDITIONS

Departament de Matemàtiques, ESEIAAT, Universitat Politècnica de Catalunya, Colom, 11, Terrassa(08222). Barcelona, Spain

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Abstract

Abstract

This paper investigates the spatial behavior of the solutions of the Laplace equation on a semi-infinite cylinder when dynamical nonlinear boundary conditions are imposed on its lateral side. We prove a PhragménLindelöf alternative for the solutions. To be precise, we see that the solutions increase in an exponential way or they decay as a polynomial. To give a complete description of the decay in this last case we also obtain an upper bound for the amplitude term by means of the boundary conditions. In the last section we sketch how to generalize the results to a system of two elliptic equations related with the heat conduction in mixtures.
- Phragmén-Lindelöf alternative /
- dynamic boundary conditions /
- Laplace equation
MSC: 35B30;35B40;35B53;35J65

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References

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