TY - JOUR
T1 - ASYMPTOTIC BEHAVIOR FOR WAVE EQUATIONS WITH SPACE-DEPENDENT DAMPING IN A WEIGHTED ENERGY CLASS
AU - Sobajima, Motohiro
N1 - Publisher Copyright:
© 2023 American Institute of Mathematical Sciences. All rights reserved.
PY - 2023/7
Y1 - 2023/7
N2 - In this paper, we discuss diffusion phenomena for the wave equation with space-dependent damping. It is known that this phenomenon occurs in the constant damping case with initial data belonging to a suitable energy class. This paper clarifies that diffusion phenomenon also occurs when the damping is effective and space-dependent, and initial data belong to a certain energy class. The proof relies on an energy method involving Kummer’s confluent hypergeometric functions with a modified version of the technique of decomposition of solutions introduced in [20].
AB - In this paper, we discuss diffusion phenomena for the wave equation with space-dependent damping. It is known that this phenomenon occurs in the constant damping case with initial data belonging to a suitable energy class. This paper clarifies that diffusion phenomenon also occurs when the damping is effective and space-dependent, and initial data belong to a certain energy class. The proof relies on an energy method involving Kummer’s confluent hypergeometric functions with a modified version of the technique of decomposition of solutions introduced in [20].
KW - damped wave equation
KW - diffusion phenomenon
KW - space-dependent damping
KW - weighted energy space
UR - http://www.scopus.com/inward/record.url?scp=85166414192&partnerID=8YFLogxK
U2 - 10.3934/cpaa.2023058
DO - 10.3934/cpaa.2023058
M3 - Article
AN - SCOPUS:85166414192
SN - 1534-0392
VL - 22
SP - 2078
EP - 2098
JO - Communications on Pure and Applied Analysis
JF - Communications on Pure and Applied Analysis
IS - 7
ER -