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3 results

GLOBAL EXISTENCE AND BLOW-UP FOR NON-NEWTON POLYTROPIC FILTRATION SYSTEM COUPLED WITH LOCAL SOURCE
JUN ZHOU, CHUNLAI MU
Journal:

Glasgow Mathematical Journal / Volume 51 / Issue 1 / January 2009

Published online by Cambridge University Press:

01 January 2009, pp. 39-47

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January 2009
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This paper deals with the global existence and blow-up properties of the following non-Newton polytropic filtration system coupled with local source: ut − Δm,pu = avα, vt − Δn,qv = buβ. Under appropriate hypotheses, we prove that the solution either exists globally or blows up in finite time depending on the initial data and the relations between αβ and mn(p − 1)(q − 1).

MINIMAL SOLUTIONS FOR A CLASS OF ELLIPTIC SYSTEMS
MARCELO MONTENEGRO
Journal:

Bulletin of the London Mathematical Society / Volume 37 / Issue 3 / June 2005

Published online by Cambridge University Press:

01 June 2005, pp. 405-416

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June 2005
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There exists a set $\cal U$ in the plane, such that elements of $\cal U$ correspond to minimal stable solutions of a two-parameter elliptic system. For points on the boundary $\Upsilon$ of $\cal U$, there exist weak solutions to the elliptic system. The paper studies the properties of the curve $\Upsilon$.

Modification of balayage spaces by transitions with application to coupling of PDE’s
Wolfhard Hansen
Journal:

Nagoya Mathematical Journal / Volume 169 / 2003

Published online by Cambridge University Press:

22 January 2016, pp. 77-118

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2003
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Modifications of balayage spaces are studied which, in probabilistic terms, correspond to killing and transitions (creation of mass combined with jumps). This is achieved by a modification of harmonic kernels for sufficiently small open sets. Applications to coupling of elliptic and parabolic partial differential equations of second order are discussed.

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3 results

GLOBAL EXISTENCE AND BLOW-UP FOR NON-NEWTON POLYTROPIC FILTRATION SYSTEM COUPLED WITH LOCAL SOURCE

MINIMAL SOLUTIONS FOR A CLASS OF ELLIPTIC SYSTEMS

Modification of balayage spaces by transitions with application to coupling of PDE’s