Geodesic
On multidimensional exact solutions of the nonlinear diffusion equation of the pantograph type with variable delay
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 3, pp. 359-374

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We consider a multidimensional pantograph-type nonlinear diffusion equation with a linearly increasing time delay and scaling with respect to spatial variables in the source (sink). It is proposed to construct exact solutions by the reduction method using two ansatzes with a quadratic dependence on spatial variables. The dependence of the solution on spatial variables is found from a system of algebraic equations, and the dependence on time is found from a system of ordinary differential equations with a linearly increasing delay of the argument. A number of examples of exact solutions are given, both radially symmetric and anisotropic with respect to spatial variables.
Keywords: nonlinear diffusion equation of pantograph type, increasing time delay, reduction
Mots-clés : scaling in spatial variables, exact solutions 
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     title = {On multidimensional exact solutions of the nonlinear diffusion equation of the pantograph type with variable delay},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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     number = {3},
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A. A. Kosov; È. I. Semenov. On multidimensional exact solutions of the nonlinear diffusion equation of the pantograph type with variable delay. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 3, pp. 359-374. http://geodesic.mathdoc.fr/item/VUU_2024_34_3_a3/