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arXiv · 2106.03564

Well-posedness for some third-order evolution differential equations: A semigroup approach

Flank D. M. Bezerra·Alexandre N. Carvalho·Lucas A. Santos
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Abstract

In this paper, we discuss the well-posedness of the Cauchy problem associated with the third-order evolution equation in time $$ u_{ttt} +A u + \eta A^{\frac13} u_{tt} +\eta A^{\frac23} u_t=f(u) $$ where $\eta>0$, $X$ is a separable Hilbert space, $A:D(A)\subset X\to X$ is an unbounded sectorial operator with compact resolvent, and for some $\lambda_0>0$ we have $\mbox{Re}\sigma(A)>\lambda_0$ and $f:D(A^{\frac13})\subset X\to X$ is a nonlinear function with suitable conditions of growth and regularity.

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Flank D. M. Bezerra, Alexandre N. Carvalho, Lucas A. Santos. 2021-06-07. Well-posedness for some third-order evolution differential equations: A semigroup approach. https://arxiv.org/abs/2106.03564

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