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Science in China Series A: Mathematics : Volume 60

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The varieties of Heisenberg vertex operator algebras

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Blow-up of p-Laplacian evolution equations with variable source power

Weighted polyharmonic equation with Navier boundary conditions in a half space

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Blow-up of p-Laplacian evolution equations with variable source power

Content Provider	Springer Nature Link
Author	Zheng, Zhi Qi, YuanWei Zhou, ShuLin
Copyright Year	2016
Abstract	We study the blow-up and/or global existence of the following p-Laplacian evolution equation with variable source power $${s_j} = {\beta _j} + \overline {{\beta _{n - j}}}p$$ where Ω is either a bounded domain or the whole space ℝ$^{ N }$, q(x) is a positive and continuous function defined in Ω with 0 < q $_{−}$ = inf q(x) ⩽ q(x) ⩽ sup q(x) = q+ < ∞. It is demonstrated that the equation with variable source power has much richer dynamics with interesting phenomena which depends on the interplay of q(x) and the structure of spatial domain Ω, compared with the case of constant source power. For the case that Ω is a bounded domain, the exponent p − 1 plays a crucial role. If q+ > p − 1, there exist blow-up solutions, while if q $_{+}$ < p − 1, all the solutions are global. If q $_{−}$ > p − 1, there exist global solutions, while for given q $_{−}$ < p − 1 < q $_{+}$, there exist some function q(x) and Ω such that all nontrivial solutions will blow up, which is called the Fujita phenomenon. For the case Ω = ℝ$^{ N }$, the Fujita phenomenon occurs if 1 < q $_{−}$ ⩽ q $_{+}$ ⩽ p − 1 + p/N, while if q $_{−}$ > p − 1 + p/N, there exist global solutions.
Starting Page	469
Ending Page	490
Page Count	22
File Format	PDF
ISSN	16747283
Journal	Science in China Series A: Mathematics
Volume Number	60
Issue Number	3
e-ISSN	18691862
Language	English
Publisher	Science China Press
Publisher Date	2016-11-15
Publisher Place	Beijing
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	p-Laplacian blow-up variable source power Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Blow-up analysis for parabolic p-Laplacian equations with a gradient source term

Blow-up of the Solution for a p-Laplacian Equation with Positive Initial Energy

Blow-up theory for symmetric critical equations involving the p-Laplacian

Existence and nonexistence of global positive solutions for a weakly coupled P-Laplacian system

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Convergence to Separate Variables Solutions for a Degenerate Parabolic Equation with Gradient Source

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Blow-up of p-Laplacian evolution equations with variable source power

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