STUDY OF SOLUTIONS TO A FOURTH ORDER PARABOLIC EQUATION∗
Keyword(s):
This paper studies a fourth-order parabolic equation ut + ε(unuxxx)x − δ|uxx|muxx = 0 with the boundary conditions uxx = 0, u = l and the initial condition u(x, 0) = u0(x). The existence of solutions is obtained from the semidiscretization method. When the initial function is close to a constant steady state solution, the uniqueness of the bounded solutions is obtained. Finally, by the iteration technique from its semi-discrete problem, the solution exponentially converges to a constant steady state solution as the time tends to infinity.
2021 ◽
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pp. 124979
2009 ◽
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pp. 2127-2132
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2013 ◽
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pp. 249-269
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2019 ◽
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pp. 1745-1755
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