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<p>We consider a two-dimensional space-fractional transient groundwater flow equation with nonlinear head-dependent recharge and extraction source function, a constant specific storage and variable hydraulic conductivity. First, we solve the approximate problem instead of the original one (the approximate and original differential operators are <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-associated). We prove that it has a unique solution in a certain generalized function space. Then we compare the solution of the original problem (assuming it exists) and the solution of the approximate problem, and prove that they are <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-associated. In the solving procedure we use the theory of Colombeau generalized uniformly continuous semigroups of operators.</p>

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Two-dimensional space-fractional transient groundwater flow equation with nonlinear head-dependent recharge and extraction source

  • 期刊论文

  • 发表日期：

    2026年7月24日

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  • Miloš Japundžić,
  • Danijela Rajter-Ćirić

摘要

We consider a two-dimensional space-fractional transient groundwater flow equation with nonlinear head-dependent recharge and extraction source function, a constant specific storage and variable hydraulic conductivity. First, we solve the approximate problem instead of the original one (the approximate and original differential operators are \(L^2\) L 2 -associated). We prove that it has a unique solution in a certain generalized function space. Then we compare the solution of the original problem (assuming it exists) and the solution of the approximate problem, and prove that they are \(L^2\) L 2 -associated. In the solving procedure we use the theory of Colombeau generalized uniformly continuous semigroups of operators.