Technical Transactions

<abstract><title style='display:none'>Abstract</title>The uniqueness of classical solutions to inverse parabolic semilinear problems together with nonlocal initial conditions with integrals, for the operator <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_2353737XCT.17.138-6889_eq_001.png"/><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:mrow><mml:mfrac><mml:mo>∂</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mfrac><mml:mo>∂</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>+</mml:mo><mml:mi>v</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>-</mml:mo><mml:mfrac><mml:mo>∂</mml:mo><mml:mrow><mml:mo>∂</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:math><tex-math>\sum\limits_{i,j = 1}^n {{\partial \over {\partial {x_i}}}\left( {{a_{ij}}\left( {x,t} \right){\partial \over {\partial {x_j}}}} \right)} + v\left( {x,t} \right) - {\partial \over {\partial t}},</tex-math></alternatives></inline-formula>, <italic>x</italic>=(<italic>x</italic>1,..., <italic>xn</italic>), in the cylindrical domain <italic>D</italic>:= <italic>D</italic>0×(<italic>t</italic>0, <italic>t</italic>0+<italic>T</italic>) ⊂ℜ<italic>n</italic>+1, where <italic>t</italic>0∈ℜ, 0 &lt; <italic>T</italic> &lt;∞ are studied. The result consists in the introduction of nonlocal conditions with integrals.</abstract>

Abstract

Institute of Mathematics, Faculty of Physics, Mathematics and Computer Science

Institute of Electrical Engineering and Computer Science, Faculty of Electrical and Computer Engineering

Keywords

<article-title>Uniqueness of Solutions to Inverse Parabolic Semilinear Problems under Nonlocal Conditions with Integrals</article-title>

Uniqueness of Solutions to Inverse Parabolic Semilinear Problems under Nonlocal Conditions with Integrals

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Editor-in-Chief Jacek Pietraszek, Cracow University of Technology, Poland Managing Editor Tomasz Kapecki, Cracow University of Technology, Poland Editorial Advisory Board Prof. PhD. Jan Błachut – University of Liverpool (Great Britain) Prof. PhD. Eng. Tadeusz Burczyński – Silesian University of Technology (Poland) Prof. PhD. Leszek Demkowicz – The University of Texas at Austin (USA) Prof. PhD. Joseph El Hayek – University of Applied Sciences (Western Switzerland) Prof. PhD. Zbigniew Florjańczyk – Warsaw University of Technology (Poland) Prof. PhD. Eng. Józef Gawlik – Cracow University of Technology (Poland) Prof. PhD. Eng. Marian Giżejowski – Warsaw University of Technology (Poland) Prof. PhD. Eng. Arch. Sławomir Gzell – Warsaw University of Technology (Poland) Prof. PhD. Allan N. Hayhurst – University of Cambridge (Great Britain) Prof. PhD. Eng. Maria Kusnierova – Slovak Academy of Sciences/Slovenská Akadémia Vied (Slovakia) Prof. PhD. Eng. Krzysztof Magnucki– Poznan University of Technology (Poland) Prof. PhD. Eng. Herbert Mang, dr h.c. - Vienna University of Technology (Austria) Prof. PhD. Arthur E. McGarity – Swarthmore College (USA) Prof. Ivor Samuels - University of Birmingham, UK Prof. PhD. Eng. Günter Wozny – Technical University in Berlin/Technische Universität Berlin (Germany) Prof. PhD. Eng. Roman Zarzycki – Lodz University of Technology (Poland) Editors Dariusz Borkowski, Cracow University of Technology, Poland Mateusz Gyurkovich, Cracow University of Technology, Poland Radomir Jasiński, Cracow University of Technology, Poland Stanisław Kuciel, Cracow University of Technology, Poland Stanisław Młynarski, Cracow University of Technology, Poland Paweł Pławiak, Cracow University of Technology, Poland Andrzej Winnicki, Cracow University of Technology, Poland Michał Zielina, Cracow University of Technology, Poland Language Editors Timothy Churcher, Big Picture, United Kindgdom Mairead Coyle, Ireland Robin Gill, United Kingdom Technical Editors Dorota Sapek, Cracow University of Technology, Poland Aleksandra Urzędowska, Cracow University of Technology, Poland Małgorzata Sikora, Cracow University of Technology, Poland Publisher De Gruyter Poland Bogumiła Zuga 32A Str. 01-811 Warsaw, Poland

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Technical Transactions

Uniqueness of Solutions to Inverse Parabolic Semilinear Problems under Nonlocal Conditions with Integrals

Ludwik Byszewski y
Ludwik Byszewski y
Tadeusz Wacławski
Tadeusz Wacławski

Publicado en línea: 26 May 2020

Volumen & Edición: Volumen 114 (2017) - Edición 8 (August 2017)

Páginas: 165 - 175

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Technical Transactions

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Technical Transactions

Uniqueness of Solutions to Inverse Parabolic Semilinear Problems under Nonlocal Conditions with Integrals

Ludwik Byszewski yLudwik Byszewski yTadeusz WacławskiTadeusz Wacławski

Publicado en línea: 26 May 2020

Volumen & Edición: Volumen 114 (2017) - Edición 8 (August 2017)

Páginas: 165 - 175

Detalles de publicación y publicación

Technical Transactions

Vista previa del PDF

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Artículos Recientes

Ludwik Byszewski y
Ludwik Byszewski y
Tadeusz Wacławski
Tadeusz Wacławski