Initial value problems for a class of nonlinear integro-partial differential equations
Copyright policy )Initial value problems for a class of nonlinear integro-partial differential equations
Under certain regularity conditions on the coefficients, it is shown that the initial-value problem \[ \begin{cases} u_{tt}-au_{xxt}-p(u_x)_x-\int_0^t\lambda(t-s)q(u_x)_x ds=f(x,t),\\ \left.u\right|_{t=0}=\varphi(x),\;\left.u_t\right|_{t=0}=\psi(x),\end{cases} \] where \(x\in{\mathbb R}\) and \(t>0\), has a global classical solution. The proof is based on a local existence result plus apriori energy estimates.
- Lanzhou University of Technology China (People's Republic of)
Other nonlinear integral equations, nonlinear integro-partial differential equations, Integro-partial differential equations, initial-value problem, existence, global classical solution
Other nonlinear integral equations, nonlinear integro-partial differential equations, Integro-partial differential equations, initial-value problem, existence, global classical solution
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!