Asymptotic expansion of L-2-norms of solutions to the heat and dissipative wave equations

作者：Volkmer Hans^*

来源：Asymptotic Analysis, 2010, 67(1-2): 85-100.

DOI：10.3233/ASY-2010-0980

• heat equation
• dissipative wave equation
• diffusion phenomenon
• asymptotic expansion of L-2-norm

Let v(t, x) and u(t, x) be solutions of the heat equation v(t)-Delta v = 0 and dissipative wave equation u(tt)+ u(t)-Delta u = 0, respectively. The paper finds the asymptotic expansions of the squared L-2-norms of v, u and u- v as well as of their derivatives as t -> infinity. Suitable conditions on the initial values u(0, x), u(t)(0, x) and v(0, x) lead to cancellation of the leading terms of the asymptotic expansion of u - v explaining the diffusion phenomenon for linear hyperbolic waves.

• 出版日期2010