Existence and asymptotic behavior of blow-up solutions to weighted quasilinear equations
By Ahmed Mohammed. 2004
56 citations recorded by the source corpus.
Abstract Given a bounded domain Ω we consider local weak blow-up solutions to the equation Δpu=g(x)f(u) on Ω . The non-linearity f is a non-negative non-decreasing function and the weight g is a non-negative continuous function on Ω which is allowed to be unbounded on Ω . We show that if Δpw=−g(x) in the weak sense for some w∈W 1,p 0 (Ω) and f satisfies a generalized Keller–Osserman condition, then the equation Δpu=g(x)f(u) admits a non-negative local weak solution u∈W 1,p loc (Ω)∩C(Ω) such that u(x)→∞ as x→∂Ω . Asymptotic boundary estimates of such blow-up solutions will also be investigated.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a19721c356a35e84df54a9a5acbb6b83fa1d11d8
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Boundary asymptotic and uniqueness of solutions to the p-Laplacian with infinite boundary values (2007, background): “In [18], it is shown that problem (1.”