Abstract
An inhomogeneous nonlinear heat equation with exponential growth nonlinearity is investigated in two space dimensions. In the defocusing case, global well-posedness is obtained. In the focusing sign, existence of the associated ground state is proved, then global and non-global existence of solutions is discussed via potential well method and instability of standing waves is established.
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T. Saanouni is grateful to the Laboratory of PD and Applications at the Faculty of Sciences of Tunis.
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Saanouni, T. A Note on The Inhomogeneous Nonlinear Heat Equation in Two Space Dimensions. Mediterr. J. Math. 13, 3651–3672 (2016). https://doi.org/10.1007/s00009-016-0707-7
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DOI: https://doi.org/10.1007/s00009-016-0707-7