quasilinear degenerate parabolic equation,
instantaneous support shrinking,
Stefan problem,
classical solvability,
porous medium equation,
degenerate parabolic equations.
Main publications:
O klassicheskoi razreshimosti mnogomernoi zadachi Stefana pri konvektivnom dvizhenii vyazkoi neszhimaemoi zhidkosti. Mat. sbornik, 1987, t. 132(174), vyp. 1.
Klassicheskaya razreshimost nestatsionarnoi zadachi Stefana s konvektsiei. DAN SSSR, 1986, t. 287, # 1.
L_1-L_infty otsenki resheniya zadachi Koshi dlya anizotropnogo vyrozhdayuschegosya parabolicheskogo uravneniya s dvoinoi nelineinostyu i rastuschimi nachalnymi dannymi. Mat. sbornik, 2007, t. 198, # 5.
S. P. Degtyarev, “On the phenomenon of the support shrinking of a solution with a time delay and on the extinction of the solution”, Mat. Sb., 212:2 (2021), 38–52; Sb. Math., 212:2 (2021), 170–184
2013
2.
B. V. Bazalii, S. P. Degtyarev, “A boundary-value problem in weighted Hölder spaces for elliptic equations which degenerate at the boundary of the domain”, Mat. Sb., 204:7 (2013), 25–46; Sb. Math., 204:7 (2013), 958–978
B. V. Bazaliy, S. P. Degtyarev, “Classical solution of a degenerate elliptic-parabolic free boundary problem”, Zh. Mat. Fiz. Anal. Geom., 7:4 (2011), 295–332
S. P. Degtyarev, “The solvability of the first initial-boundary problem for parabolic and degenerate parabolic equations in domains with a conical point”, Mat. Sb., 201:7 (2010), 67–98; Sb. Math., 201:7 (2010), 999–1028
S. P. Degtyarev, “Conditions for instantaneous support shrinking and sharp estimates for the support of the solution of the Cauchy problem for a doubly non-linear parabolic equation with absorption”, Mat. Sb., 199:4 (2008), 37–64; Sb. Math., 199:4 (2008), 511–538
S. P. Degtyarev, A. F. Tedeev, “$L_1$–$L_\infty$ estimates of solutions of the Cauchy
problem for an anisotropic degenerate parabolic equation with double
non-linearity and growing initial data”, Mat. Sb., 198:5 (2007), 45–66; Sb. Math., 198:5 (2007), 639–660
B. V. Bazalii, S. P. Degtyarev, “On classical solvability of the multidimensional Stefan problem for convective motion of a viscous incompressible fluid”, Mat. Sb. (N.S.), 132(174):1 (1987), 3–19; Math. USSR-Sb., 60:1 (1988), 1–17
B. V. Bazalii, S. P. Degtyarev, “Classical solvability of the nonstationary Stefan problem with convection”, Dokl. Akad. Nauk SSSR, 287:1 (1986), 20–24
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