JournalszaaVol. 31, No. 3pp. 291–305

On the Unique Solvability of Certain Nonlinear Singular Partial Differential Equations

  • Jose Ernie C. Lope

    University of the Philippines, Quezon City, Philippines
  • Marian P. Roque

    University of the Philippines, Quezon City, Philippines
  • Hidetoshi Tahara

    Sophia University, Tokyo, Japan
On the Unique Solvability of Certain Nonlinear Singular Partial Differential Equations cover
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Abstract

We study the singular nonlinear equation tut=F(t,x,u,ux)tu_{t}=F(t,x,u,u_{x}), where the function FF is assumed to be continuous in tt and holomorphic in the other variables. Under some growth conditions on the coefficients of the partial Taylor expansion of FF, we show that if F(t,x,0,0)F(t,x,0,0) is of order O(μ(t)α)O(\mu(t)^{\alpha}) for some α[0,1]\alpha\in[0,1] as t0t\rightarrow0 uniformly in some neighborhood of x=0x=0, then the equation has a unique solution u(t,x)u(t,x) with the same growth order.

Cite this article

Jose Ernie C. Lope, Marian P. Roque, Hidetoshi Tahara, On the Unique Solvability of Certain Nonlinear Singular Partial Differential Equations. Z. Anal. Anwend. 31 (2012), no. 3, pp. 291–305

DOI 10.4171/ZAA/1461