On the shape of the solutions of second order parabolic partial differential equations (Q1122701)
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scientific article; zbMATH DE number 4107273
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the shape of the solutions of second order parabolic partial differential equations |
scientific article; zbMATH DE number 4107273 |
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On the shape of the solutions of second order parabolic partial differential equations (English)
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1988
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The objective of this paper is to derive some properties of the solutions of an initial-boundary value problem for the following time-homogeneous equation in one spatial dimension: \(u_ t=(a\cdot u_ x)_ x+c\cdot u.\) A typical result under appropriate assumptions states that u(t,.) has at most finitely many zeros for every \(t>0\) (see Theorem 3.2). The proofs of the theorems essentially depend on the analyticity of the solutions with respect to the time variable.
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comparison theorems
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oscillation
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zeros and growth of solutions
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initial- boundary value problem
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time-homogeneous equation
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analyticity of the solutions
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