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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
    Print publication:
    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).

  • 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
    Print publication:
    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.