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Blow-Up of Solutions to Quasilinear Parabolic Equations
Sufficient conditions for global nonexistence (blow up) of solutions of the initial-boundary value problem for a class of second-order quasilinear parabolic equations: ut−∑i=1n∂∂xi((d+|▽u|p−2), ∂u∂xi)+g(u,▽u)=ƒ(u) are ...
Erdem, D
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Existence Results for Some Quasilinear Parabolic Equations
Nonlinear Analysis: Theory, Methods & Applications, 1989A quasilinear parabolic equation is considered. Minimal regularity of the data and a natural growth condition are assumed. It is shown that if there exist a subsolution \(\phi\) and a supersolution \(\psi\) such that \(\phi\leq \psi\), then there exists at least one weak solution u such that \(\phi\leq u\leq \psi\).
Lucio Boccardo +2 more
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Generalized Quasilinearization for Quasilinear Parabolic Equations with Nonlinearities of DC Type
Journal of Optimization Theory and Applications, 2001The authors consider an initial-boundary value problem for a class of quasilinear parabolic equations whose lower-order nonlinearity is of d.c. function type (difference of two convex functions) with respect to the dependent variable. Combining the method of quasilinearization with the well-known method of upper and lower solutions together with the ...
Carl, S., Lakshmikantham, V.
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Removable Singularities and Quasilinear Parabolic Equations
Proceedings of the London Mathematical Society, 1984On etablit un theoreme sur les singularites eliminables pour des equations parabiliques ...
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On the Solvability of Double Degenerate Quasilinear Parabolic Equations
Acta Mathematica Hungarica, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fisher, Brian, Liu, Z.
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Some quasilinear parabolic equations
Nonlinear Analysis: Theory, Methods & Applications, 1991The author is concerned with finding \(u\in L^ q(0,T,W_ 0^{1,q}(\Omega))\) satisfying an equation of the form \(A(t)u+F(u,Du)=S\) with \(S\) and \(u(0)\) given and \(A(t)\) a quasilinear parabolic operator. The author remarks that in two cases results concerning existence have already been obtained, specifically when \(S\in L^{p'}(0,T,W^{- 1,p'}(\Omega)
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On Systems of Singular Quasilinear Parabolic Equations and Inequalities
Journal of Mathematical Sciences, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mitidieri, E., Pokhozhaev, S. I.
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Quasilinear Parabolic Equations in Lp
2006The paper contains a local existence and uniqueness result for quasilinear parabolic equations on a three-dimensional domain including mixed boundary conditions and discontinuous coefficients.
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QUASILINEAR ELLIPTIC AND PARABOLIC EQUATIONS OF ARBITRARY ORDER
Russian Mathematical Surveys, 1968This paper is a survey of recent results on the solution of boundary value problems for quasilinear elliptic and parabolic equations of order 2m, of divergent form. The main results in this direction were first obtained in 1961 by Vishik, Browder, the author and others, and are presented in the first part of the paper.
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A Strongly Degenerate Quasilinear Equation: the Parabolic Case
Archive for Rational Mechanics and Analysis, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andreu, Fuensanta +2 more
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