Blow-up of continuous and semidiscrete solutions to elliptic equations with semilinear dynamical boundary conditions of parabolic type |
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Authors: | Miglena Koleva Lubin Vulkov |
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Institution: | Center of Applied Mathematics and Informatics, University of Rousse, Rousse 7017, Bulgaria |
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Abstract: | In this paper we present existence of blow-up solutions for elliptic equations with semilinear boundary conditions that can be posed on all domain boundary as well as only on a part of the boundary. Systems of ordinary differential equations are obtained by semidiscretizations, using finite elements in the space variables. The necessary and sufficient conditions for blow-up in these systems are found. It is proved that the numerical blow-up times converge to the corresponding real blow-up times when the mesh size goes to zero. |
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Keywords: | Blow-up Elliptic equations Dynamical boundary conditions Steklov spectral problem Semidiscretization in space Convergence |
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