The Nonexistence of the Solutions for the Non-Newtonian Filtration Equation with Absorption |
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Authors: | Qitong Ou |
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Affiliation: | School of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,China |
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Abstract: | ![]() The paper proves the nonexistence of the solution for the following Cauchy problembegin{align*}begin{cases}u_{t} ={rm div}left(left|nabla u^{m} right|^{p-2} nabla u^{m} right)-lambda ; u^{q},&qquad left(x,tright)in S_{T} ={mathbb{R}}^N times left(0,Tright), uleft(x,; 0right)=delta left(xright), &qquad xin {mathbb{R}}^,end{cases}end{align*}under some conditions on textit{m,p,q},$lambda$, where $delta $ is Dirac function. |
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Keywords: | Non-Newtonian filtration equation Cauchy problem nonexistence. |
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