Premium
Local Solutions of Semilinear Wave Equations in H s +1
Author(s) -
Pecher Hartmut
Publication year - 1996
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19960125)19:2<145::aid-mma767>3.0.co;2-m
Subject(s) - mathematics , wave equation , mathematical analysis , linearity , class (philosophy) , pure mathematics , mathematical physics , physics , quantum mechanics , artificial intelligence , computer science
The Cauchy problem for the wave equation with power type non‐linearity ±∣ u ∣ σ *u and data in H s +1 (ℝ n )× H s (ℝ n ) is considered, where 0< s <( n /2)−1 and n ≥3. Under the growth restriction σ * ⩽4/( n −2−2 s ) in many cases the existence of a local solution with u ( t )∈ H s +1 (ℝ n ) is shown which is unique in a closely related class.