On the existence of a fundamental solution for a parabolic differential equation with unbounded coefficients
P. Besala (1975)
Annales Polonici Mathematici
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Displaying similar documents to “On the linear and quasilinear parabolic equations”
On the existence of a fundamental solution for a parabolic differential equation with unbounded coefficients
Some theorems on the estimate and existence of solutions of integro-differential equations of parabolic type
H. Ugowski (1972)
Annales Polonici Mathematici
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Explicit exponential decay bounds in quasilinear parabolic problems.
Philippin, G.A., Vernier Piro, S. (1999)
Journal of Inequalities and Applications [electronic only]
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Parabolic equations with multiple singularities
Di Benedetto, Emmanuele
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On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis
Piotr Biler, Lorenzo Brandolese (2009)
Studia Mathematica
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We establish new results on convergence, in strong topologies, of solutions of the parabolic-parabolic Keller-Segel system in the plane to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under a natural smallness assumption.
Existence of a classical solution for linear parabolic systems of nondivergence form
Masashi Misawa (2004)
Commentationes Mathematicae Universitatis Carolinae
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We prove the unique existence of a classical solution for a linear parabolic system of nondivergence and nondiagonal form. The key ingredient is to combine the energy estimates with Schauder estimates and to obtain a uniform boundedness of a solution.