On uniqueness for a system of heat equations coupled in the boundary conditions.
Kordoš, M. (2004)
Acta Mathematica Universitatis Comenianae. New Series
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Kordoš, M. (2004)
Acta Mathematica Universitatis Comenianae. New Series
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Wojciech Zajączkowski (1996)
Banach Center Publications
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Existence of weak solutions and an -estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The -estimate is proved for equations with coefficients continuous with respect to x and t in the general main part, and for diagonal systems with coefficients satisfying the Carathéodory condition.
J. I. Díaz (2001)
Extracta Mathematicae
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Robert Dalmasso (1993)
Annales Polonici Mathematici
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We study the existence and nonexistence of positive solutions of nonlinear elliptic systems in an annulus with Dirichlet boundary conditions. In particular, a priori bounds are obtained. We also study a general multiple linear eigenvalue problem on a bounded domain.
Wojciech Zajączkowski (1996)
Banach Center Publications
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We prove existence of weak solutions to nonlinear parabolic systems with p-Laplacians terms in the principal part. Next, in the case of diagonal systems an -estimate for weak solutions is shown under additional restrictive growth conditions. Finally, -estimates for weakly nondiagonal systems (where nondiagonal elements are absorbed by diagonal ones) are proved. The -estimates are obtained by the Di Benedetto methods.
Pudełko, Anna (2004)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Bögelein, Verena (2008)
Annales Academiae Scientiarum Fennicae. Mathematica
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Vincenzo Ferone, Basilio Messano (2004)
Revista Matemática Complutense
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We consider a solution u of the homogeneous Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) = g(x,u) + f, where the principal term is a Leray-Lions operator defined on W (Ω). The function g(x,u) satisfies suitable growth assumptions, but no sign hypothesis on it is assumed. We prove that the rearrangement of u can be estimated by the solution of a problem whose data are radially symmetric.
Krzysztof Topolski (1994)
Annales Polonici Mathematici
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We consider viscosity solutions for first order differential-functional equations. Uniqueness theorems for initial, mixed, and boundary value problems are presented. Our theorems include some results for generalized ("almost everywhere") solutions.
Gary Lieberman (1996)
Banach Center Publications
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Bouziani, A., Merazga, N. (2007)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Arina A. Arkhipova (2001)
Commentationes Mathematicae Universitatis Carolinae
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We prove local in time solvability of the nonlinear initial-boundary problem to nonlinear nondiagonal parabolic systems of equations (multidimensional case). No growth restrictions are assumed on generating the system functions. In the case of two spatial variables we construct the global in time solution to the Cauchy-Neumann problem for a class of nondiagonal parabolic systems. The solution is smooth almost everywhere and has an at most finite number of singular points.