Long-time behaviour of solutions of a class of nonlinear parabolic equations |
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| Authors: | Xiaochuan Liu Changzheng Qu |
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| Institution: | Centre for Nonlinear Studies, Northwest University, Xi’an, 710069, PR China; Department of Mathematics, Northwest University, Xi’an, 710069, PR China |
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| Abstract: | In this paper, the long-time behaviour of solutions of a class of nonlinear parabolic equations is studied. It is shown that the solutions of initial-boundary value problem to the equations converge to a travelling wave solution of the equation or a self-similar solution of a Hamilton–Jacobi equation under certain conditions on initial and boundary values of the solutions. |
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| Keywords: | Long-time behaviour Nonlinear parabolic equation Travelling wave Self-similar solution |
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