Solution Representations for a Wave Equation with Weak Dissipation
| dc.creator | Wirth, Jens | |
| dc.date | 2002-10-02 | |
| dc.date.accessioned | 2026-07-07T04:51:26Z | |
| dc.date.available | 2026-07-07T04:51:26Z | |
| dc.description | We consider the Cauchy problem for the weakly dissipative wave equation $$ \bx v+\fracμ{1+t}v_t=0, \qquad x\in\R^n,\quad t\ge 0, $$ parameterized by $μ>0$, and prove a representation theorem for its solution using the theory of special functions. This representation is used to obtain $L_p$--$L_q$ estimates for the solution and for the energy operator corresponding to this Cauchy problem. Especially for the $L_2$ energy estimate we determine the part of the phase sp which is responsible for the decay rate. It will be shown that the situation d strongly on the value of $μ$ and that $μ=2$ is critical. | |
| dc.description | 29 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0210030 | |
| dc.identifier | http://arxiv.org/abs/math/0210030 | |
| dc.identifier | Math. Meth. Appl. Sci. 27/1 (2004) 101-124 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65148 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35L05; 35L15; 35B45 | |
| dc.title | Solution Representations for a Wave Equation with Weak Dissipation | |
| dc.type | text |