Kelvin-Voight equation with p-Laplacian and damping term: Existence, uniqueness and blow-up

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• 作者：S.N. Antontsev^a ; ^b ; ^{antontsevsn@mail.ru" class="auth_mail" title="E-mail the corresponding author} ; Kh. Khompysh^c ; ^{konat_k@mail.ru" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Kelvin&ndash ; Voight ; p-Laplacian ; Weak solution ; Blow-up
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：446
• 期：2
• 页码：1255-1273
• 全文大小：408 K

文摘

In this paper, we consider the initial-boundary value problem for a generalized Kelvin–Voight equation with p-Laplacian and a damping term: Here class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305261&_mathId=si2.gif&_user=111111111&_pii=S0022247X16305261&_rdoc=1&_issn=0022247X&md5=4762c411de0d427747290d2d2dd9c22b">class="imgLazyJSB inlineImage" height="19" width="42" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16305261-si2.gif">class="mathContainer hidden">class="mathCode"> is the velocity field, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305261&_mathId=si3.gif&_user=111111111&_pii=S0022247X16305261&_rdoc=1&_issn=0022247X&md5=1fcbee39e622ec7032e7a8eebb6e969b" title="Click to view the MathML source">P(x,t)class="mathContainer hidden">class="mathCode"> is the pressure, ν is the viscosity kinematic coefficient, and ϰ is the viscosity relaxation coefficient (is a length scale parameter characterizing the elasticity of the fluid). The coefficient γ and the exponents p, m are given constants. Under appropriate conditions on the data, we prove the existence and uniqueness of the global and local weak solutions. Under several assumptions on the exponents p, m, the coefficients ν, ϰ, and specified initial data, a finite time blow-up and the behavior of the solutions for large times are also established.