Solution Representations for a Wave Equation with Weak Dissipation

Details Solution Representations for a Wave Equation with Weak Dissipation Solution Representations for a Wave Equation with Weak Dissipation

2002-10-02

arxiv.org/abs/math/0210030v1

Math. Meth. Appl. Sci. 27/1 (2004) 101-124

Mathematics

Analysis of PDEs

29 pages, 2 figures

Scientific paper

We consider the Cauchy problem for the weakly dissipative wave equation $$ \bx v+\frac\mu{1+t}v_t=0, \qquad x\in\R^n,\quad t\ge 0, $$ parameterized by $\mu>0$, 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 $\mu$ and that $\mu=2$ is critical.

Affiliated with

Also associated with

No associations

Rating

Solution Representations for a Wave Equation with Weak Dissipation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Solution Representations for a Wave Equation with Weak Dissipation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Solution Representations for a Wave Equation with Weak Dissipation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-165181