# Null Condition for Semilinear Wave Equation with Variable Coefficients

Serdica Mathematical Journal (1999)

- Volume: 25, Issue: 4, page 321-340
- ISSN: 1310-6600

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topCatalano, Fabio. "Null Condition for Semilinear Wave Equation with Variable Coefficients." Serdica Mathematical Journal 25.4 (1999): 321-340. <http://eudml.org/doc/11522>.

@article{Catalano1999,

abstract = {∗The author was partially supported by M.U.R.S.T. Progr. Nazionale “Problemi Non Lineari...”In this work we analyse the nonlinear Cauchy problem
(∂tt − ∆)u(t, x) = ( λg + O(1/(1 + t + |x|)^a) ) ) ∇t,x u(t, x), ∇t,x u(t, x) ),
whit initial data u(0, x) = e u0 (x), ut (0, x) = e u1 (x). We assume a ≥ 1,
x ∈ R^n (n ≥ 3) and g the matrix related to the Minkowski space. It can be
considerated a pertubation of the case when the quadratic term has constant
coefficient λg (see Klainerman [6])
We prove a global existence and uniqueness theorem for very regular initial
data. The proof avoids a direct application of Klainermann method (Null
condition, energy conformal method), because the result is obtained by a
combination beetwen the energy estimate (norm L^2 ) and the decay estimate
(norm L^∞ ).},

author = {Catalano, Fabio},

journal = {Serdica Mathematical Journal},

keywords = {compactly supported initial data; decay estimate},

language = {eng},

number = {4},

pages = {321-340},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Null Condition for Semilinear Wave Equation with Variable Coefficients},

url = {http://eudml.org/doc/11522},

volume = {25},

year = {1999},

}

TY - JOUR

AU - Catalano, Fabio

TI - Null Condition for Semilinear Wave Equation with Variable Coefficients

JO - Serdica Mathematical Journal

PY - 1999

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 25

IS - 4

SP - 321

EP - 340

AB - ∗The author was partially supported by M.U.R.S.T. Progr. Nazionale “Problemi Non Lineari...”In this work we analyse the nonlinear Cauchy problem
(∂tt − ∆)u(t, x) = ( λg + O(1/(1 + t + |x|)^a) ) ) ∇t,x u(t, x), ∇t,x u(t, x) ),
whit initial data u(0, x) = e u0 (x), ut (0, x) = e u1 (x). We assume a ≥ 1,
x ∈ R^n (n ≥ 3) and g the matrix related to the Minkowski space. It can be
considerated a pertubation of the case when the quadratic term has constant
coefficient λg (see Klainerman [6])
We prove a global existence and uniqueness theorem for very regular initial
data. The proof avoids a direct application of Klainermann method (Null
condition, energy conformal method), because the result is obtained by a
combination beetwen the energy estimate (norm L^2 ) and the decay estimate
(norm L^∞ ).

LA - eng

KW - compactly supported initial data; decay estimate

UR - http://eudml.org/doc/11522

ER -

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