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Volume 8, Issue 2
Cauchy Problem for Semilinear Wave Equations in Four Space Dimensions with Small Initial Data

Yi Zhou

J. Part. Diff. Eq., 8 (1995), pp. 135-144.

Published online: 1995-08

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  • Abstract
In this paper, we consider the Cauchy problem ◻u(t,x) = |u(t,x)|^p, (t,x) ∈ R^+ × R^4 t = 0 : u = φ(x), u_t = ψ(x), x ∈ R^4 where ◻ = ∂²_t - Σ^4_{i=1}∂²_x_i, is the wave operator, φ, ψ ∈ C^∞_0 (R^4). We prove that for p > 2 the problem has a global solution provided tile initial data is sufficiently small.
  • Keywords

Wave equation Cauchy problem global solution

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@Article{JPDE-8-135, author = {Zhou , Yi}, title = {Cauchy Problem for Semilinear Wave Equations in Four Space Dimensions with Small Initial Data}, journal = {Journal of Partial Differential Equations}, year = {1995}, volume = {8}, number = {2}, pages = {135--144}, abstract = { In this paper, we consider the Cauchy problem ◻u(t,x) = |u(t,x)|^p, (t,x) ∈ R^+ × R^4 t = 0 : u = φ(x), u_t = ψ(x), x ∈ R^4 where ◻ = ∂²_t - Σ^4_{i=1}∂²_x_i, is the wave operator, φ, ψ ∈ C^∞_0 (R^4). We prove that for p > 2 the problem has a global solution provided tile initial data is sufficiently small.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5647.html} }
TY - JOUR T1 - Cauchy Problem for Semilinear Wave Equations in Four Space Dimensions with Small Initial Data AU - Zhou , Yi JO - Journal of Partial Differential Equations VL - 2 SP - 135 EP - 144 PY - 1995 DA - 1995/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5647.html KW - Wave equation KW - Cauchy problem KW - global solution AB - In this paper, we consider the Cauchy problem ◻u(t,x) = |u(t,x)|^p, (t,x) ∈ R^+ × R^4 t = 0 : u = φ(x), u_t = ψ(x), x ∈ R^4 where ◻ = ∂²_t - Σ^4_{i=1}∂²_x_i, is the wave operator, φ, ψ ∈ C^∞_0 (R^4). We prove that for p > 2 the problem has a global solution provided tile initial data is sufficiently small.
Zhou , Yi. (1995). Cauchy Problem for Semilinear Wave Equations in Four Space Dimensions with Small Initial Data. Journal of Partial Differential Equations. 8 (2). 135-144. doi:
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